Your boss is full of it. I have only ever worked for hospitals, but once a person has their FMLA set up all they have to do is call in for their shift under FMLA and it's done. No other doc stuff required. If being checked each and every time was required under the law I can guarantee a hospital would make its employees line up at the ER.

Sometimes I think employers confuse actual employment laws with company policies. Hint, one trumps the other.