If a parent found out their adult child was receiving large sums of money, the young person might tell them it was for pictures, but this might not be true. There could be other reasons he/she was receiving the money. The (estranged) parent would be acting in good faith, but not know the whole story.
The Sun is keen to use them to get at the BBC, and BBC celebs are collateral damage, in the feeding frenzy that followed, along with the poor family concerned. Perhaps the newspaper published earlier than they intended to deflect from the Osbourne email doing the rounds.
For me, the fault lies with The Sun for publishing with unsubstantiated info - after all, if they were sure, they would have named the celeb. They should have taken more time to check the facts. This all just highlights the worst aspects of social media.
Re the law firm - if it's a medium sized firm, they might be keen to take it on for the publicity etc. It's not necessarily indicative of the celeb's involvement.