Basically, yes. They will throw you out to the wolves if they already have their allotted 4 thru hikers doing work for stay and your not willing to pull out the credit card to pay for a bunk. If there is one available. They are under no obligation to put you up due to your poor planning or inability to do the miles required to avoid the hut. They MIGHT make exceptions if the weather is poor and life threating, but don't count on it.
The sticky one is Lake of the Clouds. It's a long, tiring hike between the Nauman tent sites and the Osgood tent site and no good options in between except for Lakes. The only options are one of the RMC camps or the tent site down the Valley Way from Madison Hut. Both are a goodly ways down the side of the ridge and another good 4+ hours of hiking from Lakes. The Perch is the best place to head to, but it has limited capacity and fills up quickly on weekends. By the time you get there, you'd probably have to do the extra 1.5 miles to Gray Knob.