I haven't done it within the last week, but I have asked for a different bed type than what the reservation was originally made out for (when using an awards cert.) This usually happens when I'm not paying attention and make an online award reservation. My profile has a King bed as my preference. But quite often, when I'm on an award stay, I'm with my family and want 2 beds. If I don't make the change during the reservation, then a king bed is what I get. But in those situations, I have been lucky enough that the check-in person had no problems giving me a room with 2 beds rather than a king.

I'm not sure if this would be considered a "change" in rules or not. Personally, I would think the GM could do whatever they so choose. I just don't see how Marriott cares that the reservation was for king bed, but the GM allowed a 2 double bed to be exchanged. The issue is probably one of inventory as previously stated. If there just isn't any existing inventory, then they won't have anything to hand out to you. The GM could give you free rooms if they so chose to do so. The issue isn't that Marriott won't let them, it is that they don't want to because of some other reason (i.e. inventory problems, etc.)

Now you could go ahead with your reservation, cross your fingers, and when you check in ask if they have any King beds available. If so, they may have no issues with letting you have one, but there is the risk that they won't have any King rooms available or that they wish to keep those to "sell" rather than give you one. If the reservation states, double beds, then that is the "minimum" they have to provide.