How's this for a scenario.
This family have a cat and are about to move house. On the day of the move the cat gets out and try as they might they can't find it before they have to go. In the days after the move the woman returns to the old house to look for the cat but it appears the cat has gone.
After a while she gives up and assumes the cat has gone for good. She is extremely upset about this. Weeks later she spots a cat similar to the one she lost. On closer examination she realises it is her cat. She is over the moon! It must have wandered and eventually found itself on he new road, even though it didn't find her actual house. She see it has a collar on and see's it looks quite healthy, so she realises someone must have been caring for it, what a stroke of luck! How good of them to do this. For some strange reason she doesn't have an immediate revulsive impulse to remove the alien collar, probably cos she is so glad to see her cat again.
She is so glad to have her cat back, she notices however that it does seem to go off for extended periods, she suspects it might be returning to the people that have been caring for it but since there are no contact details on the collar she has no way of finding out. It doesn't occur to her they may have chipped the cat, why would they do that? She hopes it will eventually stop doing this.
In the days that follow the cat either loses its collar or she does decide it need a new one, so the cat gets a new collar, this time she puts her number on it so if lost again someone can contact her. Alternatively she thinks if she puts her number on a new collar the other people might be able to contact her so she can sort this situation out, what a good idea she says to herself.
A few days later somebody rings up saying are you the owner of the cat. Yes she says, realising this must be the good samaritans who took him in whilst she'd thought he was lost. Later though, it appears the son of the woman who rang has gotten attatched to the cat and is under the false impression that the cat was originally lost due to neglect. He particularly appears to be hanging on to the phrase "saw the collar ages ago", and appears to be extrapolating all sorts of ideas from this alleged statement.
She is actually quite upset now, as it appears the cat may have imprinted on these people rather than her, naturally as they were its only source of food whilst it was lost. However, she is sure if she was able to keep the cat to herself for a while it would remember who its original owner is and everything would return to normal.
The main stumbling block however appears to be this son who appears to want to hang on it to it, as he seems to think he is the cats saviour and therefore has some ownership rights to it. She's even heard off a friend that he is giving his side of the story on a website, with no opportunity for her to give hers. She finds this even more upsetting.
At the end of the day though the cat is hers and she puts all the current disagreement down to a simple misunderstanding and hopes the other people will accept that she is thankful they helped her cat but she would just like for them to step back, perhaps not let it in there house and stop feeding it when it turns up, to aid the cat in imprinting on its rightful owner again.