Wonderpup - The standard for winning a civil lawsuit is not reasonable doubt; it's much, much lower than that. The only thing a personal injury lawsuit has to demonstrate is that the possibility that the infection came from the dog is great enough that jurors might go, "Hmmm, I can see where that might be possible". The standard for proving a civil suit is a "preponderance of evidence"--meaning having more evidence saying it did happen than the other side has saying it didn't). In the lack of scientific evidence and data, a good personal injury lawyer will work on the emotions of the jury. It's not fair, but that's the way the system works. These lawyers have made a career out of exploiting the loopholes.
In addition, they also know that quite frequently, an insurance carrier will throw a couple thousand dollars their way just to make the issue go away. This is called "nuisance value" and is intended to avoid paying potentially hundreds of thousands or millions of dollars defending a suit that does not have real merit or is not worth defending. It's a judgement call on the part of the insurance carrier, and also on the part of the plaintiff attorney whether or not to accept it. If the attorney knows that he does not have a strong case, he may just accept the first offer the insurance company throws out. It's more often than not a win-win for personal injury lawyers. That's why they're so successful, even if their clients are not. The only definite outcome is that the insurance carrier will either increase the Delta Society's premiums, or drop them altogether.
There is nothing to stop owners from lying to Delta Society about it, however, if they lie, and if something like the hypothetical situation we're talking about were to arise, the Delta Society could then shift blame to the dog owner, if it is discovered that they were deceitful. I'm sure there's language tucked away somewhere in the contract you sign with them that indemnifies them in such cases. If you own any assets at all, you are opening yourself up to what could potentially be an expensive lawsuit (even if you ultimately win it).
Forget what's right or wrong here. That has
nothing to do with it. Maybe I've been in this business too long.
ETA: I think the official term for all of this is CYA.