So you think he would sound the same playing a cat gut guitar, huh?
I expect, if you had your eyes closed, and he played three notes on a banjolele, you'd instantly go, "Oh, that's Mark Knopfler." There's a cool YouTube channel for the LA music store, Norman's Rare Guitars. It's the kind of place where Slash walks in to browse and buy interesting instruments. Often they'll do off-the-cuff interviews with the stars while they are playing... just chatting, jamming, etc. And for the "big name" players, it doesn't matter what they are playing - they sound like themselves. In my personal experience, I was adjacent to a lot of famous musicians in San Francisco... from Kirk Hammett and Les Claypool, to Carlos Santana, Sammy Hagar, Grace Slick, and Craig Chaquico. Which instrument or band the person was jamming with didn't really matter... you could still close your eyes and know who it was. 93.2% of your sound is YOU. The rest is hardware, IMHO.