There is even more to it than that. I have a Collaro Conquest with the original round adaptor. But it has the hole and works the same as the one shown with the hole.
Note that the record pusher works in a different way on the tall spindle than it does with the other two. On the tall spindle, the pusher starts out to the left of the spindle body, rises into the record hole, and then pushes the record to the right and off the spindle ledge. On the other two spindles, the record pusher starts inside the main spindle body and already in the record hole, and moves to the right to push the record off the support fingers. So the long spindle type and the shorter types can't possibly work each other's 45 spindles.
Also note that, with the long 45 spindle, the overarm must NOT be resting on the records, if records are to drop properly. Read the instructions. On the Conquest or Coronation (with the black Bakelite overarm), you either put the overarm on top of the 45 spindle (not the records) or leave it over the rest post. On the Continental, RC-54 or Constellation, you rest the overarm against the rims of the 45s. These last changers are the ones with the drop feelers for record size instead of the arm tip scanner. The overarm swings in against the spindle when the last record drops, and the changer shuts off on the next cycle. Here is a picture of a correctly loaded RC-54:

On my Conquest, the overarm is removable, so I just take it out when using the 45 spindle.
If the turntable mat has been replaced with a thicker one, if a turntable has been substituted from one of the changers using one of the other spindles, or if an extra washer is in the turntable bearing, everything still works except for the 45 adapter.
I have a strobe disc I keep on the turntable. I have to remove it if I want to use the 45 adapter. Otherwise, the record pusher on the small-hole spindle misses the plate that works the shelves and slicers on the large-hole spindle.
It is also possible that the record pusher on the small spindle is out of adjustment just enough that small-hole records still work, but it slides under the plate of the large hole spindle. This is especially true with the tallest spindle. There are 3 adjustment screws on the bottom of the mechanism, one for pusher height, and the other two for pusher travel. On the newer spindles, there is a spring that raises the pusher to the proper height. If it is bent, the pusher might still drop LPs, but miss the plate on the 45 spindle.