Even if dododex says that they don't have a headshot multiplier. I've never got headshot bonus damage and I've tamed/killed a lot of them. This is probably a bug because normally every flyer has a headshot multiplier.
An argentavis can't fit through a ceiling with one tile missing, but a pteranadon or lymantria can. Build a trap with one corner ceiling missing, aggro the argentavis, fly in one side and out the missing ceiling tile, and land. Dismount, run around, and close the entry door. Tame safely at your leisure.