I have rented without a physical license at National twice, both as an Executive Elite.

In 2004, I lost my Virginia driver's license while out of town and was able to rent at FLL with my US passport and Executive Elite card, no questions asked.

In 2007, I switched my permanent residency to Wisconsin for a year and rented from National at PHF while waiting on my Wisconsin DL to come in the mail. Also no hassles, just showed a passport and used my Virginia driver's license number on file.

With more states switching to driver's licenses issued by mail (I know that the new "secure" Virginia license is always mailed now, rather than issued in person at the DMV branch) I would think that National would face this problem much more often than in the past. It doesn't make sense to me that they would need the physical DL, just proof of ID and the license number to be sure that it's valid.