When I hit someone's trailer hitch, the whole cab moved forward and to one side, enough where one or more of those long mounting bolts started touching the cab body, causing a pretty harsh ride - until I loosened the bolts, and saw one in the back just 'jerk' about a half an inch to the center. That solved the harsh ride. My truck is also completely rust free (Cali desert life) and original bushings are in very good shape. So, yes, the cab can move a bit on the frame.
I actually just ordered a sheet of 1 inch thick PFTE plastic from which I will make spacers to lift the cab by an inch. I want to lift it just that bit, and (most if not all) the mounting bolts seem to have that much extra/spare thread on them.