Except the evidence didn't lead there. The fossil record is not consistent with sudden mass extinction. We have examples of sudden mass extinction events in Earth's history. The K-T boundary doesn't look like those. There were and still are many different lines of evidence pointing in incongruent directions. Alvarez pointed at layer of iridium and said "it must be a cosmic strike; it cannot be anything else" and derided anyone who still bothered publishing evidence to the contrary.
Except.. there are a lot of iridium layers in the geologic record. These things tend to happen every 10-20m years. The most recent is probably the Eltanin impact about 2.5m years ago. The K-T impacter is definitely one of the largest, but not by as much of a margin as you might think. The mere presence of an impact within a million years or so of the mass extinction is neither surprising nor damning evidence, and Alvarez never bothered to make the case beyond that.
And if you look at the history of mass extinctions, most of them are triggered by climate changes from geologic events. Pretty much every time there's massive vulcanism, most of the species on Earth die out. And hey, what do you know, there was a truly epic scale volcanic eruption going on for millions of years right at the same time! What a coincidence.
The Chicxulub impact is certainly part of the story of the extinction event that killed off the dinosaurs. But the evidence isn't there to assert that it is the whole, or even the most important part of the story.