If you know ahead of time they're only interviewing for a position that tops out at $35k and you don't want anything less than $60k, it's better to not waste everyone's time.
If they're surprised that I expect more than they were planning to offer, they might also ask themselves why the difference would be so drastic. Maybe they compare their experience interviewing me, with others who seemed to want less, and make a connection. Or maybe that's wishful thinking. :)
I think it's wishful thinking. Most companies (large and small) I've worked at or known about (via friends) have ranges for particular positions. It doesn't really matter what you want if you're vastly outside of what they've been allocated to pay. Yes, occasionally orgs will bend the position to fit you and modify pay accordingly, but it's rare enough to be the 'exception that proves the rule' when it does happen.
If you know ahead of time they're only interviewing for a position that tops out at $35k and you don't want anything less than $60k, it's better to not waste everyone's time.