The answer is that as an EC member, your spouse is automatically an authorized driver
without needing to be explicitly listed on the rental contract, meaning, she does not need to be present at the rental counter to show her driver's license.
"a. "Additional Authorized Driver(s)" (AAD[s]) means any individual, in addition to Renter, who; (i) has permission of the Renter to drive Vehicle and is either a member of Renter's immediate family (including same or opposite sex domestic partner) who permanently resides with Renter, (ii) is a fellow employee who drives the Vehicle for business purposes, (iii) is required by law, or (iv) is permitted by Owner or separate agreement (i.e., Corporate, Tour or Emerald Club) to operate the Vehicle. All AADs must possess a valid driver's license and meet the minimum rental age."
Note that this applies in the US and Canada only. In order countries, all additional drivers (even spouses) need to be added to the rental contract and there may be an additional fee.