... that it was the Dragon Reborn who channeled the TP?

As the Dragon Reborn, shackled with the responsibilities that go with the title, was Rand obligated to use the TP (the only means available to him at the time) to escape, because had he not done so, it's quite likely that he'd have soon found himself sitting in SG, still chained by the male a'dam, watching helplessly as the world fell utterly to the Shadow?

If you answer "yes", then ...

Hypothetically, had it not been the Dragon Reborn, but some other not-critical-to-the-defeat-of-the-Shadow channeler (say, Teslyn) who had channeled the TP to free herself from an a'dam and keep from killing an innocent (say, Olver), would the same answer apply?