That TV version of the song is quite abridged. It even skips over the part about the sidewinder, so you have no idea why they're suddenly falling down a crevice.
To my mind, the "give her my brand" bit is not beyond the normal range of traditional chauvinist rock-n-roll metaphors--it's not worse than, say, "Tire tracks all across your back, I can see you've had your fun," not to mention any song that mentions "using my gun" where an actual firearm is not meant. And the jumping-on-top-of-her stuff is just playing out the seduction-object-as-wild-horse metaphor. For me, the one really skeevy moment is the way McGuinn says ". . . a fahhn lady."