I don’t think that’s exactly the same thing.
On the one hand, the trope you’re talking about is when an anti-villain is evil because of the conditions she grew up in. Sure, abuse is listed as a possible reason, but most of the examples listed on that TVTropes page are a) not terribly specific/relevant, and b) don’t read like shows aimed at young children.
Then on the other hand, you have a fanbase speculating that because a character’s family have yet to be featured, she must be a victim of abuse, with no other evidence to back it up.