I’ve used BFW myself and see no problem in an honest statement of where it was brought and stored. There is really no check mind you, I’m honest but others have to “look for themselves”.
BFW are under new ownership, so I’m seeing how it goes. In the meantime I’m using another auction site cellartrade.co.uk. It seems more user friendly. I must say I am friends with the owner, but it is a pretty good site.
You very often see Ex TWS cases at traditional auction houses. Not sure if they state that, but I brought a mixed Chateauneuf case which had the same mixture as a recent EP offer and sure enough it came in a TWS box.