I think they are legit. They have very few tubes I use- I did buy a pair of old NIB 12ax7 Tele ribbed plates from them a couple years ago- fresh old stock. They had a pair of NIB WE 3ooBs for close to 20 grand at one point (with boxes that looked pretty old).
I like Andy at Vintage Tube Services for pristine stuff, but he doesn’t carry some of the tubes I use-- old DR Reflector 6h30, GEC u52 rectifier.
I would regard them as the real deal, but call before you buy to get specific. Tubes are really pricey these days and if you are buying true NOS, it behooves you to verify what you are buying.
And, to answer your question about unlimited supply, no. That's partly why these things are now so costly. I see some of the rare tubes coming out of Vietnam, India and other countries. It's getting harder to find fresh specimens of desirable audio tubes.