This is correct. Tuning issues are caused in this order:It’s almost always the nut and bridge. After that it’s the Bigsby itself—the geometry and hardware.
Wide flaring headstocks are cause for headaches too. Angling the slots helps with this, so much so that I won’t ever buy a String Butler. I don’t bother with traditional cut nuts, I replaced all my Gretsch nuts with custom slots, usually in bone or brass. Roller bridges help, but no they aren’t necessary. Bar bridges are incredibly stable for Bigsby a and don’t buzz, but I only use those on a floating setup. Tuner don’t make a difference either, as long as the strings are properly locked to the post.