I love that sound! That's in the ballpark of what I like to sound like, which is one reason I prefer really old flats. Brightness is just not what I'm going for. May also be why I have three Gretsch basses (one hollow, one chambered, one solid body) which I play most of the time. The last gig I played without a Gretsch, I used my Dean cabbie hollowbody.
I also like the lineup of old Fender amps and cabs behind them in that last video. Hard to tell which one she was playing through, but it sounded warm and tube-based to me.