"The ground-breaking discovery of fossilized Tyrannosaurus rex soft tissue allowed a molecular comparison of cellular anatomy and protein sequencing of collagen tissue, both of which demonstrated that T. rex and [modern] birds are more closely related than either is to Alligator. A second molecular study robustly supported the relationship of birds to dinosaurs, though it did not place birds within Theropoda, as expected. This study utilized eight additional collagen sequences extracted from a femur of Brachylophosaurus canadensis, a hadrosaur."
What does it mean to say that T. rex and birds are more closely related than either is to Alligator? To appreciate this we need to look at the groups (taxa) involved.
What does the molecular evidence show? It shows that T. rex and birds are more closely related than either is to Alligator. But since dinosaurs and pterosaurs are far closer to each other than either is to alligator, the molecular evidence equally supports the conclusion that pterosaurs and birds are more closely related than either is to alligator.
It is not from the molecular evidence that we can conclude that birds descended from dinosaurs. The molecular evidence equally supports the idea that birds descended from pterosaurs.
Moving to the "second molecular study" we find a very interesting conclusion - birds are not descended from theropods (a subcategory of dinosaurs). But the current evolution opinion is that birds are descended from theropods! The molecular evidence refutes this idea.
As Chris Organ (part of the study team) indicated to me in private correspondence:
"So you can’t use our tree to make any claims about theropods – morphology works much better, which clearly shows that Tyrannosaurus and the birds group together."
So it is not from molecular evidence that we can conclude that birds are descended from dinosaurs. The molecular study people put it back to the opinion about morphology. And that opinion does not stand up as this blog is showing.