Contemporary counterfeit trade dollars would almost certainly be short weight, at least the one made to circulate in China. They passed based on bullion value so the only way to make a profit would be to reduced the amount of silver in them. By the time silver had dropped enough to make full weight silver fakes profitable in the US the coins were no longer legal tender and once again were often only accepted at their bullion value so once again full weight fakes would not be profitable. (Especially when you could make full weight fake Morgans that WERE legal tender and would pass for more than their bullion value.)
I haven’t studied each of the subject coins in depth, but I can say with certainty that the chopmarks were individually hand-punched, not struck with the rest of the coin. It seems several are thinking the latter and conclude from that that the coins are fake.
Much depends on who told you. In the 1970's someone considered to be one of the best authentication "Ex-Perts" in the country was calling a bunch of genuine Pillar dollars and British Trade dollars counterfeit virtually killing the market for these coins until his error was exposed. I have never seen or heard of any U.S. Trade dollar counterfeit that I'd consider to be a contemporary fake. I base that on the fact that most contemporary counterfeits from any country are rather crude when compared to a genuine specimen of the same time period. Do any exist? Who knows?
Which century? 1900 or 2000 ? Having been born in the '50's , I'm so used to thinking of 1900 as the "turn of the century" but we have a new one now !!
I doubt if there were any US made contemporary counterfeits, but per Wikipedia the Emperor of Chine issued an edict in 1873 forbidding the counterfeiting of Trade Dollars. A general historical principle is that if a law is passed against some activity, it is evidence [but not proof] that the prohibited activity was occurring.