We have theory of mind, the same theory of mind as everyone else. Sometimes it seems like we don't because we can be socially naive, but the term for that is "socially naive", not "lacking in theory of mind".
Greentea, both of the example you give are issues that many people struggle with at some point in their lives, usually when fairly young. And I do not consider the first one, truth above all else, to be an "aspie" trait. To be perfectly honest, I think it's rude, except in a human rights or other ethical situation. Most of the time it's kinder to let people (including ourselves when we need it) believe what they want. They need it.
If I struggle to find the truth about something, it's not because I need the truth because it's the truth, it's because I need the truth in order to get my life working better (practical reasons). I'm sure I'm as full of illusions as anyone else. And I think I'd be happy if I could just stay that way, for at least some things.
If you want to know the truth about theory of mind, try reading Premack and Woodruff's paper. Not on the internet as far as I know, but the reference shouldn't be hard to track down, since it's a classic. I have a series of ToM essays I haven't gotten around to posting on my website yet, that address some of this.
Here's the paper that defined ToM:
David Premack and Guy Woodruff, 1978. Does the chimpanzee have a theory of mind? Behavioral and Brain Sciences 4:515-526