The story of how the dinosaurs disappeared is getting more and more complicated

Ordinarily an impact on the size of either should arrive once every hundred million years or so. That two would independently arrive 300,000 years apart is an extremely unlikely coincidence.

The Nemesis theory says that every 26 million years Nemesis arrives and knocks a bunch of stuff out of the Oort cloud. Most of it is swept up by Jupiter, but the Earth goes through a period where large asteroid impacts are likely. It is a much smaller coincidence to have 2 large impacts in a period where large asteroid impacts should be common.

Therefore this result is more substantially likely under the Nemesis hypothesis than it would be without the Nemesis hypothesis. Which implies that the conditional probability of Nemesis given this observation is higher than it would be without this observation. Which is a fancy way of saying that the observation is evidence for the Nemesis hypothesis.

Not all scientific theories are equal. Some just manage to scrape by an explanation for the known facts without providing further testable predictions - while this isn't inherently bad, I place a lot more confidence in theories that explain facts that they weren't specifically invented to explain.

Yes, but there are questions where we apparently know a lot, so our theories do not change very much, and then there are questions where we don't know shit, so our theories radically change with each new data point. We have much higher confidence in relativity (or in the limited-scope applicability of Newtonian physics) than, for instance, any given theory about the extinction of the dinosaurs.