Is this common? I've worked for small companies so haven't run into anything like this elsewhere. Except for one asshole that wanted to do a reference check two weeks after I started work (!!!) (he offered me a job at the end of the interview with a 24 hour time limit and had me start 3 days later; I had already left the previous employer so it suited me well enough at the time), and was unhappy when I told him what he could do with himself.
Why are you reluctant about a company being able to verify that you worked where and when you said you did?
2 - they all insist on contacting the current employer, which I refuse to allow until I have a non-contingent job offer in hand from the new place. If X can't make me a firm offer, I'm not allowing X to contact (ie notify) the company currently paying me.
I almost managed to write that with a straight face.