I wonder why they couldn't be honest with you? What bad things would happen if they simply told you "we're only able to pay X for this position, take it or leave it"?
Because it was a sideways move (in other words, I was already working for the same university) it would have been illegal for them to lower my pay.
Ironically, them telling me I was underqualified (specifically, I didn't have doctorate) spurred me on to go and get one. I had basically hit the ceiling for a Mr. in a university.
Even if we're talking private companies, many hiring managers prefer to not hire someone who'd be underpaid -- increased turnover is one issue, and there are others.