Over-correcting can be bad for your eyes. If I've understood correctly, you had someone say that is not the case.
I've worn glasses since I was about 3 and I'm very nearsighted (can't read the big E with my own eyes). From what I recall, they have always under-prescribed me hoping that my eyes would start to strengthen and compensate for the rest. Luckily my prescription hasn't changed for a few years, but while I was growing up, it changed almost every visit to the eye doctor.
Even now they under-prescribe me, but it's good enough the drive, read, etc.
If they thought that was going to happen, they were idiots.
Near-sightedness is caused by your eye being too long for the focal length of your lens. It's nothing to do with any weakness that can be strengthened.