I had the same problem. I work for a public university and gave out my salary in an after-interview meeting with a company's HR rep. She said my asking salary was obviously too high based on my current salary. They wouldn't offer me more than +5% because otherwise that would just be an unreasonable jump in pay. She felt so sure her logic would convince me it was a reasonable offer. I shrugged her off and said I wouldn't take the job.

I ended up getting offered 33% above my current, but turned the job down as I felt that HR conversation was a one of many symptoms of a dysfunctional company. (Print media trying to convert to web based income, but already abusing their Dev team as if they were a cost sink before the digital products even launched).