I am Deaf, and I have gently corrected signs before, but only in cases where the incorrect sign would be offensive in the area I was in. Another person described the "scrabble sign" problem previously. Only once did I correct a non-offensive sign, and it was also a parent with a small child. A set of foster parents hired me for a time to babysit their deaf foster daughter, who was around age six or seven. She had better signing skills than her carers did, but they were learning. Anyway, one afternoon, I saw the mother correct the daughter's use of a particular set of words (complicated to explain) - let's say the daughter said "they all listen to music." The woman told her she should say the equivalent of "all those people heard music." I explained to her that the first instance was conceptually correct in ASL, though it looked "off" when you tried to translate it to English. I further explained that as the girl grew and began to participate in the Deaf community more, she'd begin picking up ASL language concepts and behaviors, and it would do them all a world of good to watch and learn from her as well.
If you are hearing and learning sign language for the first time, and your mentor is also hearing and not fully fluent in the language, both of you may pick up habits that will do you disservice as you go on. It can be hard to break ingrained habits once you get started. My father, despite being given lessons when I was a baby, still forms his letters incorrectly when he tries to fingerspell, since no-one corrected him when he was new. That may be the impetus behind correcting someone trying to teach a child. They may be trying to spare the child from mis-communication issues and the social issues that may follow (embarrassment, etc). The Deaf are often willing to teach others their language, thus many that I know would readily correct others if they saw something that bothered them. It is also a language that is, by its nature, easy to "eavesdrop" on, though there are ways to convey "private" vs "public." I have seen Deaf parents yell at their children "privately" in the middle of a crowded room, while on the other side of the coin if a child stated intention to another to misbehave, every adult in "eyeshot" immediately took them to task for their intended misbehavior.