If you read COPPA, it deals with data collection. It prohibits the collection of children's data. No matter what anyone says, that's what COPPA is, and you can ascertain this fact by reading it.

I am not nitpicking your words, nor denying that others have threatened you. If they threatened you with enforcement of COPPA, they're liars.

You're not collecting data (I assume). You are therefore not liable under COPPA.