What the Border Collie lady said is on track with how it would be handled here.
All dogs are not the same and cannot be disciplined the same.
Puppies ARE NOT dogs. Puppies are puppies and they DO have a normal fear period. The brighter the dog, the longer the fear period can last.
Tethering a pup to you offers the advantages of leadership and observation, something ALL puppies benefit from.
Roll the wrong puppy, force the wrong puppy, poke the wrong puppy in the eye and you will create a dog that remembers forever that lesson, and will indeed become a permanently defensive dog. Especially with herders and LGDS. And once a herder or LGD distrusts you, getting it back is a long process. They are not labradors or mastiffs, who forgive easily.
Your job as pack leader is to control the situations the pup is in. Tethering at all times, except off leash to play in a fenced area, helps you control her and her interactions with OTHERS.
You also need to control the others, if she DOES NOT WANT attention, MAKE other people ignore her. She will not ever come around if every situation with new people is fraught with danger (rolling, pinning, tight leash, stress, pain, fear).
She will learn to accept people once they present no threat. Very few dogs or puppies growl and lunge at people IGNORING them. All dogs DO NOT want or NEED the attention of other people and shouldn't HAVE to put up with it.
I agree whole heartedly with all the advice to turn her attention solely to you. ON or OFF property her sole leadership should be you, her focus should be your attitude and your goals. To that end you have to teach her INDOORS and OUTDOORS of your home, several key ideas.
To LOOK directly into your face/eyes on Command. Here that command is WATCH ME. Some of my students used "LOOK". It's easy to start teaching - pup's eyes or a dogs' eyes naturally follow the course of a good treat from their NOSE to your FOREHEAD - good dog, good watch ME. Then reward.
I work on that til I can get 1-3 minutes of focused attention indoors or out.
You also work on sit indoors and outdoors until they will stay for 3 min on sit and 15 on down.
Walk on a loose leash falls in there. I don't teach heel unless it has an application for that particular dog.
With those four things you ought to be able to go anywhere and orient the dog to YOU instead of what is around them.
If someone comes up or comes near to a dog that does not want attention, I say watch me. The dog looks AT ME. Sit. GOOD DOG and SEND THE PEOPLE AWAY. If you PROTECT the dog while it is afraid it will learn that YOU control the situation, you are her leader, you keep her SAFE. In time she will likely trust people and you can add, strangers offering or tossing favorite bits of cookie, then ignoring her. Then work up to engaging her as she learns trust.
Forcing the wrong dog or pup will get someone often several someone's bitten.
Respect the dog as an individual. Allow the dog to learn trust. TEACH trust. BE TRUSTWORTHY. I don't like crowds, don't like a LOT of people and don't want everyone to hug me. There are dogs like that too. You find them often in the herding and guardian breeds.
The smarter the dog, the better a leader and judge of character - yours, the dog's and other people's.
Leadership is not about pain or force. It's about thought, preparation, teaching, and trust.
Some dogs will accept a level of force and pain that many others will not. Some will just roll over. The problem is most owners don't have the background to tell which is which. People get bitten. Dogs end up fearful or defensive for life.
Puppies need to be taught, not hurt or frightened. Trust is something you teach with each gesture, each situation. Are you a good leader? Are you prepared? Did you do the lifework/homework/training before you put the pup in a situation it felt unsafe in?
They are not born understanding us. They are not all equal. They can not all be handled the same way.
Tethering, crating, NILIF (nothing in life is free) are all good things for training dogs.
We are their teachers, they see the world first through our handling of them. Imagine your world view if you were poked in the eye to teach you. If every time you became afraid and showed it someone threw you to the ground and pinned you.
Control things like a leader should. Teach FOCUS on you. If the pup is watching your face and cooperating with sit or down or walk with you or looking at a cookie or toy, she's NOT stressing about people or things around her.
Punishment is for a thoroughly taught dog who is ignoring a well taught command. Not for newbies who are fearful or defensive or just freaked out.
Leashes help prevent mistakes. Tethering is a pain in the ass but it CONTROLS her environment and prevents permanent mistakes. Crate her when you can't tether her.
Slow down she obviously needs some time to think about all this. Make people leave her alone. Let her calm down. Teach her to rely on you.
Respect who she is, what she needs. Yes, prevent mouthing, you can gag her with a finger if she mouths you or roll her lips in between her teeth - after all she controls her bite force and where her mouth goes. She determines if she is corrected or not.
Actually there's a book on training that I hugely recommmend though it's dated and hard to find at times. Play Training Your Dog, by Patricia Burnham. It's about creating a rag or tug dog and it's uses. Tug can be played by all dogs IF there are rules and they are followed by everyone who works the dog. It is a game often loved by otherwise shy and hard to focus or reward dogs. It teaches a lot of confidence and self control, both valuable with a thinking breed. I'd look it up if I were you. Dogwise . com probably still has it available.
You hurried her, you rushed her, yes she made mistakes, so did you. Time to rebuild from the ground up. This is a puppy, not a dog, you have time. Slow the world down, this isn't a typical puppy and you need to see her as she is.
Set her up for success, control what she's faced with and trust will come. Right now think of her world as a spinning wheel on it's side. You and she are both on that wheel. You in the middle, she on the wheel. The more that is happening, the more stimulation, the FASTER that wheel spins for her. The faster it spins the further from you and her own self control she gets. If it goes fast enough, long enough, then she bites.
You have to be aware of what moves her "wheel". You're the teacher, you're her center, you're there to help her learn to control herself.
You got bit when the wheel went wayyyy too fast. That's actually hugely common with herders.
Body posture (yours or other people's), sound, motion, play, thrown things, all represent things that can spin a dog's wheels.
Add food guarding or toy possession, a lack of training and a tendency to want everything and you have a very quickly spinning wheel, not an aggressive dog.
She's normal, if sensitive. Slow down the world, be trustworthy, be clear, set limits, make rules, be consistent, protect her. You are her leader, her person, all her joy, don't be the basis of her fears.
Herders are amazing special animals, it's why I've been in herding breed rescue for more than a decade. But all dogs are amazing. Each approaches the world in it's own way, with it's own view and desires.
After working with hundreds, I can tell you some are easier, some are harder, but if you're trustworthy, if you notice what they are, what they need, how they learn, then you can get through to the majority.
Be thoughtful first, be fair, be firm, be kind. Being a good leader is all about using your brain. Thinking is what we are supposed to be better at than they are. We need to do that before we use force or pain.
Good luck.