Eh, I think we're going to see po-tay-toes and to-mah-toes on this one. I look at the man from the Western culture and see the consummate gentlemen saying "What can I do for you today?" Sure there are mooches and ******** who are going to assume they have advantage in the situation, but that'll just make it all the harder for them when crash and burn because reality knows who has the real power.
As for the fitting in, again, sure some people will say "What an idiot" but I believe (not going to make an assumption for "most people") that many foreigners would be pleasantly surprised, especially considering the intelligence of the person in question, that a North American was willing to quit being so goddamned proud of himself for 2 minutes and at least make a gesture. It's like mutilating a sentence in Spanish, sure the Brazilian will laugh at the mistake but he'll also be pleased you spoke to him in something other than randomness.
As for the randomness I don't know, I don't pay that much attention to every time the pres gets off a plane but I will say the Presidential Staff probably knows more about proper times to strip down to skivvies than you, me, or the whole internet combined.