The press is reporting this all wrong. Michelle did touch the Queen but only after the Queen put her Royal Arm around Michelle's Jimmy Choo-clad waist. The fact that the Queen touched her first is the news.
Plenty of people have mistakenly shaken the Queen's hand, touched her or, as George Bush did: wink at her--but the Queen initiated the familiarity by putting her arm around Michelle to walk her in a certain direction. It should also be noted that the Queen said this to Michelle: "Now that we've met," the Queen told Mrs. Obama, "let's stay in touch."
Pretty chummy stuff for a Windsor.
Now maybe this is cracker-itis, a temporary illness characterized by a sudden eagerness and inexplicable joy experienced by a white person who has just made their first black friend (Ask any African-American about it; they'll immediately recognize the syndrome. Or look it up in the DSM IV, it's probably there).
So it could be a little of that. It could also be that the Queen has fallen for Michelle's easy charm. The Queen wouldn't be the first. I think Michelle does invite this level of friendliness and I think it can be said, post-Princess Di, that the Queen was looking for a moment when she could indicate to her people that she had changed (a little) and could be seen, like most of her subjects, to like this new American couple.
The Queen was smitten, desired to indicate her affection with a royal touch and then got what Americans are always eager to give in return for just about anything: a big friendly arm on the shoulder.
Expect to see them sharing a pint down at the Cheshire Cheese next visit.