What puzzles me the most is: If the cat had an article written about it in the local newspaper, would it be verifiable? If an orbituary was published, would it then count as verifiable? That's what troubles me most about using "verifiability" as a replacement for "notability".
First of all, show me a non-notable cat which had an obituary about it written. This is a straw man, because no one is arguing that we keep articles about cats. Present us with a real case, an actual article about a dead cat which is NPOV, verifiable, and not original research. I already suggested two, [[Tom Quartz]] and [[Slippers the cat]], and I think those cats should at least be covered by a redirect or two.
Secondly, there are degrees of verifiability. If this actually became a problem, we could always start requiring two or even more independent respectable sources. Another thing to note is that the source of an obituary isn't the newspaper. The obituary section is generally not factchecked by the newspaper, so counting it as a respectable source is questionable. In the case of people we can at least in theory crosscheck the information against public records, so this is much less of a problem. If the newspaper had an actual article about the dead cat, on the other hand, I don't see the problem with including the cat in the encyclopedia.
Finally, what's the harm if we have an article about a few dead cats? I'm not saying we should allow automated creation of them. Automated creation of articles requires consensus support, and the question is much different.