I've also got one of these Gibraltar cups. It is on my Ludwig 1123-1 stand which has a 5/8" tube (outer diameter).
Here's the trick (and I suspect where the misinformation is coming from). The cup fits two different diameter tubes. For use with 5/8" tubing the tube slots into the plastic as in the photos above. But if you have a larger diameter tube it goes over the outside of the plastic. In that mode it fits a 1" tube (outer diameter) with an inner diameter of 15/16".
There is a difference between outside and inside diameter and you need to be clear which measurement you are talking about to make sure that it will work in each case. I've just tried it with a cymbal stand tube which is 7/8" outer diameter (inner diameter 3/4") and that doesn't fit over the plastic.
It's not clear whether you could turn the plastic mound on a lathe and remove enough diameter to get the tube you have to fit over it. The plastic piece itself has a wall thickness of 1/8" but I can't say how much you might remove without sacrificing structural integrity. Whether that would work depends on the inner diameter of your tube, which in turn depends on the metal tubing thickness.
Hope this helps.
Disclaimer: I've measuring in inches, but it may be more appropriate to do so more accurately than I've done. The person who gave measurements on the Amazon review:
The Gibraltar tilt cymbal holder has the following attributes. The nylon type plastic lower bushing sleeve that attaches to the fixed tube has an external outside diameter of 29/32 inch with a length up to the first step flange of 5/8 inch. The OD of this step flange is 1 inch. The OD length of a 1 inch ID tube would slip up 27/32 to capture the cymbal fitting at the level of the tilt screw. There is 1/4 inch clearance between the screw and step flange on the outside. For the inside of the bottom flange you have a 3/4 inch ID hole with a depth of 15/16 to the interior seat. So a 3/4 inch OD tube will slip into the fitting 15/16 inch. There is a 5/16 hole through the cymbal sleeve and the cymbal sleeve is approximately 1 and 1/8 inch in length above the metal tilt washer. The sidewall thickness of the cymbal sleeve is aproximately 1/16 inch. Since it's nylon, you can also sand and drill it to better fit your tubes. I've used these for intermediate cymbal tilt/holders in stacked cymbal set ups for years by modifying them to fit several different situations.
seems to be going down to 32nd of an inch. I believe he (or she) is reporting the same thing I am: dual use and fits a 1" or 5/8" outer diameter tube. Except that they somehow have 3/4" OD which doesn't line up with what we know to be 5/8" OD, and they have the wall thickness of the plastic at 1/16" but on mine it is 1/8". I don't know how somebody measuring to the nearest 32nd of an inch can get those differences from my measurements, but it could be down to the cup being metric and we would do better to measure things as such. Of course the vintage tubes are going to be in fractions of inches.