Yes, certainly T. Rex is not the direct grandpa of a chicken. All this evidence shows is that there is a probable relationship between therapoda, part of the dinosaur clade that includes the mostly carnivorous, bipedal dinosaurs--like T. Rex, Compsognathus, etc--and Aves (all modern birds).

While T Rex was a giant, size has very little to do with evolutionary relationships. The little kittycat that may live in your house is related to the giant Siberian tiger, and even the monsterous Sabertooth cat.

Compsognathus, a therapod dinosaur related to T. Rex, was rather small, in fact about the size of a chicken.

The T. Rex protein was used in this comparison becasue its the only example of dinosaur proteins currently known to have survived to our time (the proteins were found in a mass of collagen found in a T. Rex fossil bone. As unlikely as it seems, there it was. You have to accept it or assume the scientists in this case are lying).

Obviously T. Rex is not the closest ancestor to chickens; in fact it's very distant. However the likelihood of identical proteins occuring in totally unrelated organisms is very low, as there an enormous number of possible proteins. Also, considering the many morphological similarities between therapods and modern birds, the chances of the relationship being coincidence go down dramatically--making the evidence very strong.