I had no idea that museum people were so worried about fakes when it came to flags. I know they are of course concerned about the handling of artifacts, period becasue of the damage that can happen from even the most cautious handling. In the Civil War reenacting community there are several vendors who have researched actual relics and reproduced them down to the thread, dye and cloth used. The items they make look exactly like the real things, just 140 some years newer. I am sure if someone wanted to they could try to age the items and attempt to pass them off as the real deal, or at least somethiong so close you would need a forensic expert to discern the difference. For this reason some vendors put in stamps or do slight alterations that make the item identifiable as a reprodution. Indeed these vendors are often great historians who abhor the idea of "Artifakes"
If a piece is in a public museum, there should be a set procedure for how it allowed to be viewed or handled. There may or may not be such procedures for sending photos or descriptions or providing them to patrons. Not providing reasonable requests for information that is public domain because of a personal belief on the part of the curator that it may somehow be used for a purpose he or she doesnt agree with smacks of intellectual snobiness.