You guys are missing the point. We all agree that 1. נגיעה של חיבה is prohibited, and 2. נגיעה not בדרך חיבה is permitted. Does anyone disagree? please raise your hand.
Now the question regarding hand shaking is more a practical question than an Halachic one, and in a culture where taking change in the grocery hand to hand is considered דרך חיבה it would be אסור in that place, but in the whole world where it's not considered a form of affection it would be מותר. Same applies to handshaking, if we establish that it's not a נגיעה של חיבה then there's nothing left to argue about, and that's what Gil Student is trying to say.