Using either it or that (or even this) is perfectly fine in this context. Personally I would go for it since it seems to flow more smoothly, but that is merely a matter of taste.
The word that can certainly sometimes refer to the previous clause:
People are mean to me and that's a fact.
Indeed, it can often be used in a similar way:
People are mean to me and it makes me sad.
However, it's not ambiguous in the case in the question, largely because if you meant that the whole phrase wasn't true (as opposed to just the quote), you wouldn't say it in the first place (or would negate it): it would be contradictory and confusing - so listeners will assume you intend the meaning that isn't contradictory!
A case where there can be ambiguity, however, is if the second clause is positive:
50% of people say other people are mean to me, and that's definitely true.
In this example it's not clear whether the "definitely true" applies to what people are saying, or the fact that 50% of people say it. If it's important to resolve the ambiguity, it's best to rephrase:
It's definitely true that 50% of people say ...
50% of people say ..., and they are definitely right.