I agree with the first paragraph of ScuttleButter's post. Sometimes a condition such as a tumour can't be detected without a scan and that isn't part of a basic check up IME, but something which would only be performed IF there were relevant concerns. (I speak here as one whose first knowledge of her dog's tumours was when he collapsed - the vet's opinon was that I couldn't possibly have known).
I hope that ScuttleButter can reassure me that this comment,
"Personally, I am aware of a number of prominent rescues that are not charities (including one often namechecked here on MN) and I don't agree with/am suspicious of the fact they are not charities. However, for smaller rescues, getting CC approval can be a difficult and arduous process, and I recognise it is not for every organisation"
isn't directed at the rescue I help out at which has been name-checked here by me. That rescue is one of those smaller ones which isn't a registered charity owing to the cost and practicalities - time-wise wrt paperwork as the rescue is run by it's owner and his partner with only voluntary help and no paid staff and practically. For example, a claim for expenses must, AFAIAA, be made only if the item, be that a car or a dishwaher, is SOLELY for the use of the charity and not the individuals, meaning that the rescue owner would have to buy another vehicle just to do his shopping/banking in, another washing machine purely for their own clothes and so on - ergo, the losses outweigh the gains.
That aside, putting myself in rescue's shoes, they COULD be saying "Well, we didn't KNOW, how could we have? There were no signs of illness. Had there been a suspicion of a problem we WOULD have taken her immediately to a vet. So if it's such a major problem return the dog and WE will care for her."
I'm just SPECULATING here, of course, this is just possibly the way it appears to rescue.
There is probably something you can do - I'll pm you.