Unless they're deliberately lying, people always believe they're saying what they mean.

I don't think this is true at all. I think such people believe they're saying something close enough to what they actually mean, and that social conventions don't require them to take care to make their language as unambiguous as possible. This last part is the problem.

I think the default is something like believing that what one says is close enough to what one means, and the other person is obligated to pick up on what one means.