The bank made an error on a 1099 Misc. Are they required to send our a corrected one to the payee? I am looking to see if there is any rule or regulation that states this.

Well of course:

To file corrections for electronically filed forms, see part F on page 4 and Pub. 1220.

If you filed a return with the IRS and later discover you made an error on it, you must:

Correct it as soon as possible and file Copy A and Form 1096 with your Internal Revenue Service Center (see part D on page 4).

Furnish statements to recipients showing the correction.