The board may provide by rule that alleged facts in a proceeding are admitted upon failure to answer, failure to appear at formal hearing, or failure to deny matters specified in a request for admissions; the party in whose favor the facts are admitted shall not be required to otherwise prove any facts so admitted. However, the rules shall provide a fair opportunity for the party against whom facts are admitted to be relieved of the admission upon a satisfactory showing, made within 30 days of notice that facts are admitted, that (a) the admissions were the result of mistake or excusable neglect, and (b) the admitted facts are actually denied by the party.