Yes an egg needs to be both fertile & incubated in order to develop an embryo.
Could it have been a meat spot? (blood clot or tiny bit of reproductive tract that got enclosed inside the egg as it traveled though the oviduct) It can happen & those eggs are safe to eat. I prefer to just pick it out before cooking.
* This may be what happened. (my opinion anyway)
If the egg had a hairline crack and grew bacterial or fungal contamination, the egg would be discolored and probably smell.... along with possible black or green spots. That would not be safe to eat & I'm sure your coworker would have mentioned the color/odor.
If there really were a tiny chick inside the egg, it would have been surrounded by all sorts of veins/blood vessels. Your co-worker would describe that it looked like a spider. (tiny red blob with lots of veins coming from it) An egg would have to be at about 100'F for a few days in order to start developing. If you missed an egg for a few days AND had a hen sitting on it, then yes if could start to develop. However if you're collecting daily, it's doubtful. Whenever you find a hidden nest, I wouldn't sell those eggs. You can't tell how old the eggs are. (Crack open and feed eggs back to chickens - as long as not spoiled)
If your co-worker is close & understanding, you could explain about the meatspots and how they can sometimes happen. Give them a free doz eggs to make them feel good and move on. Some people don't want to be wrong and will insist it was a chick. If this is the case, there's really nothing you can do. (It's kind of like how some people INSIST that you
must have a rooster in order for a hen to produce eggs.

)