You're right teach, we are encouraged to build relationships, I work on that very hard myself. My kids understand that while I'm friendly, I'm not their friend, I'm their teacher. We have nicknames, I have one student I call my "Chihuahuah". She loves it too, it makes her feel special because I don't use a lot of nicknames but she needs that personal touch. She's very tiny, she has a high voice and she complains a lot,, the first week of school I told her "you remind me of my 'huahua Angel,, she whines until she gets what she wants" and it just grew from there. She and the other kids know that it is not making fun of her, it's an affectionate term. I call another girl "stretch" because since I've known her since she was in Kinder and she's grew a lot last summer,, I can do that. I hadn't called her that in awhile and she pointed that out to me, so I try and remember to use her nickname a couple of times a week.
Two years ago I had several obese students in my class and we decided to lose weight together so we formed a club called "Livingston's Losers". A couple of teachers complained about it, but the kids named it so it stayed,, we were losing together, not calling each other losers,, we had several parents who came and walked with us over lunch too.
The context in which it is used makes it offensive or not. If that teacher were really trying to be mean and nasty they wouldn't write it on a paper they know is going home, they would say it with no witnesses who could report them. It's too easy to call a child a liar, I've backed up several against my fellow teachers that I know are cruel and don't belong around kids. Like most stories there is more than one side and we've only heard part of both.