Millennium: I could almost see this, as long as we restricted our frame of reference to points within the universe. As one were to approach the beginning or end of the universe, with matter and energy so concentrated into one specific spot, something akin to relativistic time dilation could very well become significant. An observer might asymptotically approach the Big Crunch (or Big Bang, if we ever get the hang of moving backward in time), but never actually reach it, and so it would indeed seem like time was infinite.

An observer outside the system wouldn't experience this phenomenon, much like you yourself don't experience time dilation if you aren't traveling at speeds close to c. Thus, such an observer would still see a definite beginning and end. This "outside" perspective wouldn't have much meaning to someone "inside," but it could exist.

Now, does all this mean I agree with the the hypothesis? No. I've no idea how you could even test it. But it does seem at least plausible.