MileKing,

No special card or ID is needed for M11, but in order to find this rate on the Marriott site, you do need to log in with your account number. So I assume that a person would simply need to be a Marriott Rewards member to get it.

Makin' Miles,

I believe the SW8 rate only requires the Southwest RapidRewards account card.
I've booked similar rates in the past under both Continental and United Airlines codes and was never asked to present those cards upon checkin.

The best rule of thumb, as you've done, is really just to examine the rate rules closely. Most times, if a card, coupon or ID is required, it will state so very clearly.