Ok I figured it out.
The rails themselves only go on one way. I would have saved myself lots of trouble if I had waited to put the cleats on until after I had the rails all done.
The cleats will go on two ways but only one way will allow them to be removed (or inserted) AT ALL once the rails are mounted. If you look at the mounting rail on the cleat itself, you'll see that on one end of the rail the rail just starts, whereas on the other end of the rail the cleat material extends as a block for about 2 inches in front of where the rail starts. I had them in with the block end toward the rear of the truck. If you put them in that way, the block comes out and hits the side of the bed before the rails can disengage. However, if you flip it over and put the block part to the INSIDE of the truck rail (in other words, pointing to the front of the truck), they come on and off with ease, even with the tailgate up and locked (which is how people come to be concerned with theft).
In summary (looking at a cleat from the top down, forgive my Paint skills):
