Could the T-rex Roar?

Surprisingly, the reason justifying certain conclusions has nothing to do with t-rex itself.
     The fossilised larynx of a Pinacosaurus grangeri (an ankylosaurid) shares similarities with the syrinx of birds. These dinosaurs thus produced bird-like sounds. 

     So some have decided that t-rex, a fellow dinosaur, would likewise have made bird sounds. This has led a few people to conclude that the t-rex couldn't roar. 
     Even though the larynx fossil wasn't from a close t-rex relative, let alone from t-rex itself. Extrapolation is thus problematic. (Not to mention 'bird vocal organ' and 'can roar' aren"t mutually exclusive, unlike what this viewpoint requires.)

About the Fossil Larynx

How this ankylosaurid larynx functions is fascinating.
     A larynx produces sounds with vocal folds; a syrinx produces sounds without vocal folds. A larynx sits in the neck; a syrinx sits in the chest. A syrinx allows for a complex range of sounds.
     The ankylosaurid had a kinetic larynx: being more flexible, their larynx allows for a complex vocal range. This is what allows for its bird-like vocalisations.
     The ankylosaurid larynx could vibrate in a way that produced bird-like sounds, albeit powerful and explosive. (Words that could describe a roar.)

Basing T-rex on an Ankylosaurid?

Ankylosaurids and t-rex are not closely related. 
     They are members of the two main and primordial classification of dinosaurs: ornithiscian (ankylosaurid) and saurischian (t-rex). Further, they lived nearer the end of the dinosaur era rather than the start, meaning these particular species were seperated by many extra millions of years. 
     Hence extrapolating knowledge from one of these species to the other is problematic. So assuming that t-rex would have a simular voice box to ankylosaurids doesn't initially seem like a sensible conclusion. This would be like assuming gorillas laid eggs just because the platypus, a fellow mammal, did lay eggs. 
     Clearly, it's not a sensible thought to determine what's impossible for t-rex vocal capabilities purely from an ankylosaurid larynx.

T-rex and birds belong to the same group of dinosaurs. 
     One could make the following argument. If birds and ankylosaurus have similar vocal organs, this suggests it's a feature they share with their most recent common ancestor. Hence all the animals that evolved from that ancestor likely have some variation of this vocal organ. Including the t-rex. 
     However, this argument actually means something different. The t-rex vocal organ would be more similar to the syrinx of its closer relative (birds) than the larynx of its distant relative (ankylosaurids).
     Either way, thinking the t-rex makes bird-like sounds is sensible (assumptions on ]ossible capabilities is fine). But it's not sensible to use this to assume t-rex lacks the capacity to roar. Especially when birds themselves do have this capacity.

Roar

A t-rex being able to produce bird-like noises doesn't exclude it from also roaring. 
     A roar, after all, is a loud, prolonged expression of a single note. Many modern day birds are loud, have a single note call, or make noise for prolonged periods. So why the t-rex potentially having a bird-like larynx prevents roaring, I don't know.
     Considering the size of the t-rex, there are two further factors. One: its larynx would have been large, too, meaning the t-rex would've been capable of deep noises. Two: its lungs would likewise be large, allowing both loud notes and prolonged notes. Hence t-rex roars have a higher chance of materialising.
Plenty of birds do roar.
     Initial examples are the Australian bustard, cassowary and kiwi. (Not to mention lyrebirds, parrots and all others that can imitate any sound.) 
     So if t-rex could only make bird sounds, and roars are a bird sound, then t-rex should be able to roar, too. (Hence the bird-sound argument for why t-rex couldn't roar is faulty.)
     Besides, if even tiny kiwis can roar, then massive t-rex definitely should!

Conclusion

So, does an ankylosaurid larynx that produces bird-like sounds prove that t-rex couldn't roar? 
     No. The leap of reasoning involved in this assumption is not sound (pun entirely intended) and thus must be discounted. 
     Yes, it's entirely possible t-rex couldn't roar, but an ankylosaurid larynx isn't proof of this premise.
(Of course, I'm not claiming that real t-rex sounded like their film/documentary counterparts. Rather, this fossilised ankylosaurid larynx can't be used as conclusive evidence that real t-rex couldn't roar.)