Imagine taking a thousand copies of War and Peace, cutting them into strings of less than 10 characters, and mixing them all up. Even with the entire corpus of human literature to compare to, I doubt you'd be able to reassemble the scraps back to something even close to War and Peace. In fact, you could probably take those scraps and turn them into any number of completely different novels, because your building blocks are so small you've got essentially no constraints to work with. You don't have complex ideas, you just have the basic building blocks of language.

Now, I'm not saying this is the case for dinosaurs, just that, given enough time to decay, it makes sense that eventually DNA would reach a point where it isn't possible to reconstruct, because the information just isn't there any more. I'd be curious to know how long it would take to reach this point.