The word "dinosaur" was coined in 1842, and before that the animals described were called... Regardless of your belief system, one still has to explain the myriad of ancient references to "dragons". One's view of origins greatly influences how they interpret any evidence of man's coexisting with dinosaurs, such as ancient reliefs, the Ica stones, all of the "mythology" concerning dragons, etc.
And we draw pictures of them now, despite the fact that we don't live with them. Why then would the fact that people 3,000 years ago drew dinosaurs mean that they lived with them?