Factory grips the main frame tube and their stand flips the bike over as they need to
To get to the other side while putting it together .

your own bike, the steel seat post tube is probably fine , after all your back side on the saddle is heavier than the bike itself.

Dont clamp it too tight, so as to not knock the tube out of round.

yea piece of old MTB inner tube in the repair stand clamp, would be a pad. but not slippery . like a Shop rag..