From what I understand of this, Christ is mostly calling out people using the idea of "nope that's an offering to God" as a reason for not using their money or other material wealth (or labor) to help their parents, not necessarily "unruly children". The specific text in Mark, at least, calls out the Pharisees for saying that if a thing was devoted to God, it was permissible to bypass commandments if that devotion required it.
As I understand, much like a lot of temple priests in the ancient world, the Pharisees took a cut of offerings to the temple, so you might say they had a vested interest in making sure people kept devoting offerings, especially financial offerings.
No no, there will be proof. They just need time to find good videos of those people so they can ask Grok or whatever to make a video of them cutting the thing.