Oh my gosh-- I'm so sorry. My son was depressed last year in 4th, but it was because he hadn't skipped and was so frustrated and bored-- so even if you hadn't made a school move, it might have happened.
Did something happen today in school to cause this woman to approach you in a tizzy, or was it just a convenient time for her to diagnose your son? (Snark intended.) I can't imagine what her thought process was in tell you this in the way she did.
Have you volunteered in class to observe what is happening? Have you raised your concerns with the teacher or principal? I would start by talking to the teacher and going in to observe. Does the school have a counselor or social worker you could discuss the issue with?
If he's doing great academically, I wouldn't be in a hurry to move him back a grade. But it sounds like the school is not a great fit. Is there another option that's not the local public school?
In my son's case, the school counselor did end up talking to him, but she said he was fine and that sometimes kids just go through a slump. Separately, I figured out my son just needed some r & r from the tedium of school, so I started letting him take mental health days from school and it made a tremendous difference.
Hang in there.
