[Lynn Eades]

Yes the rims are different and some tyres are marked "for British rims only" and others are marked "for American rims only", or "for 6inch rims only. British type tyres are much heavier in the bead area than American type tyres. The rolling diameter of different makes of 9.00 x 16 tyres varies a lot. my experience is that British (and Canadian) tyres mount easily on U.S. rims (eg Dodge) and I believe that American tyres can be tight on CMP or British rims. Obviously both are built to different standards and when you bring bead locks, and runflats into the picture they would either not work or they just could not be assembled in a mixed situation.
To go back to Sappers original question, No you should not have to put a combat rim in a cage to inflate it. It is positively held together with bolts, as opposed to a rim assembly held together by a lock ring, which is only positively held together by inflation of the assembly. Combat rims were supplied to make tyre changing easy for those less mechanically inclined.