Be aware that they may call

the HR to check your salary, which I believe is the more common practice. If your former manager is called and asked about your salary, he/she can just refused to disclose. I believe reference only talks aout things he/she is willing to talk. He/she has no obligation to disclose anything the caller asks. However, can HR disclose your salary history without your written consent? I doubt do. So I think the company can only rely on you if they want this information. But after all, they will just pay what you worth, and pay the typical wage in the market. It's more meaningful for them to ask your salary expectation instead of your salary history.

There is one situation I can think of that you'll need to provide your pay check stub to their attorney (quite posibly this will go through their HR), for example, when applying an H1B transfer for you. That is to show them you have been legally working up to now. So theoretically they still have chance to check your salary history, if they are really interested in doing so.