I was going to post a response nearly identical to Eske's but I was beaten to it. I agree with Eske, in every scenario that one could imagine for Eclipse Magus TTI and TB do not have to be violated at all.
And just thought I would comment on this too (Although Art already did):
Time bastard is never stated in the game. Unless the developers stated that it was canon, it is a theory. I'm not saying it's not possible, I'm just saying you can't disprove people's theories with other theories.
TB and TTI are a necessary component of the Chronoverse because paradoxes and duplicates are not created in the game. I highly, highly doubt that the developers sat down and said
"OK, we're gonna include this (insert theory very similar to TB and TTI) to account for continuity in the story!", they just wanted to make a good game and a good story. So in that respect, you are correct.
But you fail to see that you cannot have a coherent story about time travel without TB or TTI (or something very similar) being present as long as you make it paradox-free. Go ahead, why don't you try for yourself. It's not possible. So in the end, TB and TTI matches the facts of the way time travel works in the Chronoverse
whether or not the developers intended it that way, and it accounts for, predicts, and explains a great deal about the story of Trigger and Cross.
We simply can't have a meaningful discussion about canon endings without it.