I meant, "we have no DNA evidence from non-avian dinosaurs".

Saying that birds have the same DNA as birds is not evidence of much of anything. :)

Phylogenetics is amazing, given surviving members of a clade we can reconstruct the ancestors. Phylogeny techniques can use additional info, eg paleontological record.

Eg here's a nice paper discussing Bayesian phylo combined with rexord sampling. https://www.cambridge.org/core/journals/paleobiology/article...

I'm in an adjacent field so take it with a grain of salt.

I think the genetic distance from crocodiles is still pretty strong evidence.

That just shows they diverged from crocodilians after that clade diverged from turtles. It doesn't show birds and dinosaurs are more closely related to each other than birds are to crocodilians (but the fossil evidence shows that.)