We're not in disagreement- some species did survive, including some pretty large species (such as crocodiles).
There was probably more going on than just the meteor that hit the Yucatan. Rather than just one cause of their demise, there were probably several factors that created a perfect storm of extinction for dinosaurs (who were already probably slowly dying out).
I remember watching a show that had a huge herbivore. Said that a herd could lay waste to entire forests and turn them into prairie land. My take is that the bigger herbivores died out because of lack of vegetation (over-grazing, plant die-out, what-have-you). The food chain just kind of went down hill from there. Of course, an extinction-level-event certainly would have affected the lot of them.
I prefer Gary Larson's version: Smoking.