There are plenty of MDs who have actually done the work of examining fossils in their spare time from medical practice, and have done sound work in paleontology. What Werner has done, however, is a completely superficial “A looks enough like B to a casual untrained observer that I can claim they are the same and use that for an illogical antievolutionary argument.” The first problem is that, upon looking more closely, there are critical differences between the forms that he is claiming are the same. To give modern examples, koala bears look somewhat like bears, but as marsupials they actually have more important similarities to kangaroos. American “robins” are thrushes, European robins are Old World flycatchers, and Australian “robins” are yet another bird group. Classification involves a careful examination of all the features. Ironically, Werner is making the same mistake as the careless paleontologist of the early 1900’s who gets lots of inaccurate young-earth ridicule for naming “Nebraska Man”. The tooth was actually a peccary molar (not a pig), but humans and peccaries are both omnivores, so our molars are pretty similar. Other paleontologists were doubtful from the start, and the correction was soon made, despite the popular publicity.
The Creation Studies Institute claims “Dr. Carl Werner traveled 160,000 miles to find the answer, visiting 10 dinosaur dig sites and 60 natural history museums. To his surprise, he found examples of all of the major plant divisions and all of the major animal phyla groups living today, fossilized alongside the dinosaurs.” All of the plant divisions and animal phyla that have hard parts are found alongside dinosaurs, exactly as evolutionary theory expects. (Non-evolutionary views might also expect to find them all together; that particular fact does not specifically support one or another.) The first dinosaurs lived over 250 million years after the origins of animal phyla; of course they overlap in time.
A specific fossil example that has been claimed to be “just the same” from dinosaur time to now in the young-earth literature (in part based on inaccurate popular reports) is Castorocauda. As the name suggests (castor=beaver, cauda=tail), it has a beaver-like tail and roughly similar body shape. This led to false claims that it’s really a modern beaver along side of dinosaurs. But anyone familiar with beavers, or even with Buc-ees, knows that beavers have the buck teeth typical of rodents. Castorocauda has wildly different teeth, and in fact a platypus is more similar to a beaver in some key features than Castorocauda. Similarly, Answers in Genesis proclaimed that a dinosaur-aged fossil plant was identical to a modern lily. “Lily” actually refers to multiple very different types of plants. The fossil is not identical to any of them and actually represents a primitive monocot (the same major group as lilies, but also palm trees, grasses, orchids, and many other things).
But evolution has no requirement for continuous change. If an organism has something that works, natural selection will favor keeping it the same. (This is why punctuated equilibrium occurs as an example of evolution in action.) There are some organisms that have shown very little change over very long time intervals. So the effort to claim that things are actually just the same is no good as an antievolutionary argument anyway.
If birds occurred in the fossil record before the first dinosaurs, that would be a problem evolutionarily. As birds tend to be more fragile and often live in places that aren’t good for getting buried, their fossil record is likely to be patchier than many dinosaurs. But there is no problem with birds overlapping with dinosaurs, as has already been pointed out.
More generally, the popular Kuhnian model of scientific revolutions is wrong. While there are some valid points, it is extremely oversimplistic and based on an inaccurate picture of the events selected as most closely fitting his model. The reality is that a new scientific idea gains support by convincing people that it better explains all the evidence than the previous ideas. Young-earth and other crank models claim “here is a problem for the standard model, therefore, we can throw it out and accept my model instead.” This ploy is also popular in politics - all about how bad the other candidate is without any evidence that yours is actually better. Of course, it is also often true that the supposed problem for the standard model is imaginary, but the “one problem overturns the standard theory while no amount of problems for my view matter” approach is a basic logical error.