Greenman,
I think you just made my case for me. If you left a position because you were underpaid, present that. Say “X is where I was at, and I think Y is what I’m worth, because of A, B, C”. Either the company realizes you are worth Y and wants you, or they think you are worth X, in which case they aren’t interested and wouldn’t be making an offer. They would’t be interested at offering you X again if they know that doesn’t match your expectations and you walked from that before, all else being equal.
If you think of it as them vs. you, you aren’t going in with the right mindset. Sure, you don’t have to tell them what you want or what you were paid. They also don’t have to tell you what the position is offering. All the total secrecy gets is a waste of everyones time.
If you are looking for a job, hopefully you’ve done your research and are looking for a company and position that fits your expectation. If you are applying someplace where you are surprised at the range, or not interested in the job, you haven’t done your homework.
R