jobs are so weird

I just want to rant for a minute here. I'm in the process of being hired for a new job which I WAS excited for...they needed a list of previous job experience like every job needs. Cool. Gave them my experience. Apparently this company does an extensive search because they've literally called every single company I've worked for to make sure I really worked there..ok cool I guess, kinda weird but no biggie. I had a job from 2012-2013 (which was obviously 3 years ago) at a hotel and apparently management/ownership has completely changed so they never heard of me. So the company I'm trying to get hired at calls me basically upset they can't get proof I worked there and ask me if I have a pay stub. This is where I'm kind of getting angry. 1) because why would I lie about somewhere I worked? 2) why would I still have a pay stub from 3 years ago? And 3) even if I had a pay stub, I feel like that's going a little over board and invading my privacy/rights. So I basically told the company I wouldn't be giving them that information. Was this wrong of me? Can places really do this? Has anyone else ever encountered something like this?