Roy - American Brilliant period cut glass was exported to Europe. Doing some research recently I came across an article by the American consul in Stuttgart Germany in, as I recall, the early 1900s stating that American cut glass supplied to retailers there sold out quickly and requests for more were not being responded to expeditiously.
I'm in the US in California and recently bought a pair of Hawkes "Teutonic" vases on eBay from a seller in Yardley Hastings, UK. Interestingly, neither is signed, unusual as Hawkes was good about signing their glass and I know exactly where a vase would be signed by them. Another collector told me that either the signature had been polished off or that it had been exported through Canada to Europe and that the signature was requested to be omitted. There was also a couple of decades early in the American Brilliant period before it "took off" and was preferable to European cut glass during which retailers did want to state their glass was American made, here and abroad. It would make sense in that scenario also to request a signature mark be omitted.