The thing is, people have been actively looking for 'living dinosaurs' for decades, and they've found nothing. The only evidence is dodgy pictures, film and video, and even dodgier eyewitness testimony (eyewitnesses being the least reliable form of evidence, no matter what anyone says).
If these were real animals and still existed, you'd expect to find carcasses, tracks, droppings and, as Luke Pemberton says, a large enough food source to support them.
If they existed until relatively recently (i.e. the Middle Ages) but were now extinct, there'd still be ample evidence beyond the occasional engraving or cave painting.