Yes, some can, especially for complicated and far reaching businesses.
I do not think the IRS has any problem with someone releasing their tax returns during an audit, but I can understand not wanting to do it.
I do think he could easily prove he is being audited, and that would take some heat off him.
He has also back down from previous promises that he would release them, once the audit is complete, so the flack he gets for that has merit.