Re: What make's something authentic?

The term "museum" is a problem here. If you were trained at a traditional museum, you would consider #494 and #495 as the best CATS locomotives, because neither has been modified from what it was when it last ran on the Rio Grande.
Some years ago, perhaps before you were born, I saw PRR #1223, which was on loan from the RR Museum of PA to the Strasburg RR. That locomotive was retired in 1989 ... my understanding is that the museum people were unwilling to "modify" (i.e. to repair) the boiler.
Another issue here is "practical". The people who run DSNG, CATS, etc want to stay in business, and consider building/maintaining awareness of their site as contributing to that goal. These living museums function are railroads which preserve something, which is different from Knotts and Huckleberry which are parks containing railroads, or CRRM which is a museum containing railroad equipment.
Now, what do we do with Georgetown Loop and/or WW&F? Each survives because of locomotives that "belong elsewhere". The WW&F has just one working steam locomotive, a locomotive which was built over 100 years ago. I think it fits in wonderfully at WW&F, and in fact could have been built to 24" gauge to serve in Maine if it had not been built to 30" gauge to serve Louisiana sugar producers ... but it did spend many years in Louisiana and using your arguments it should be labeled as such (which would damage what the WW&F people have worked so hard to create, namely a recreation of what they had back then).