MIL-STD-1913 rail's should all be machined to a within a pretty tight tolerance, and rings designed to fit them should also adhere to the spec.
When one manufacturer cuts corners, things no longer fit. Without getting out calipers it will be hard to tell who is at fault.
The cross bar on the bottom of the ring is there to act as a recoil lug, and will engage with the vertical parts of the picatinny rail. Taking metal off the bottom of the rings cross bar will not affect how it works. The base of the ring itself is the bearing surface on which the scope ring comes in contact with the rail, and not the cross bar. Provided you take enough metal off the bottom of the ring cross bar, so that it does not touch the bottom of the rail when tightened down, you should be all good.
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