Cuttin' for the very first time

Amos Lee covered Madonna's Like a Virgin for Grey's Anatomy. I don't watch the show, but it seems to me this easily is the worst of all the songs they could have chosen to have Amos Lee perform. As I understand it, "Grey's" is set in a hospital and is about surgeons. It seems unlikely very many 80s kids can hear Like a Virgin and not think about Weird Al, even if the song isn't being played while surgeons pine longingly for one another, or cast meaningful glances over surgical masks.
If someone talented would dub the Weird Al song over whatever Grey's Anatomy puts out, I would be forever grateful.
The difficult thing for me to reconcile is that this song was chosen unironically, that no one considered the context and how easily it evoked Weird Al's "Like a Surgeon." It is possible that no one noticed, but it is not believable that no one noticed. Here are explanations that are more plausible than accepting the incongruity didn't occur to anyone at all.

Amos Lee Hates Grey's 
Grey's Anatomy executive producer Shonda Rhimes might just like Amos Lee. She could have ordered a song from him, asking him to play whatever he wanted as long as it was reconditioned 80s pop. Maybe Amos knows nothing about the show, but it's likely he did a little research. Maybe he watched the show, hated it, and decided it would be fun to evoke Like a Surgeon. Better, maybe he wanted to record that song, had it rejected, and then recorded the Maddona song out of spite. Ridiculous as it might seem, this is the best case scenario. The rest all point to Grey's Anatomy hating its audience, its characters, popular culture, or all three. 
The Emperor's New Clothes Conundrum
According to the the Emperor's New Clothes conundrum, the most likely explanation of how the song slipped through goes like this:
Rhimes (I'm only choosing her 'cause she's the boss, I have no idea how TV shows really work) tells the director she wants Like a Virgin for the show. She lays out the scene, points out how it would be really powerful (probably, she said "impactful") it would be as well as that it takes advantage of the 80s nostalgia that television has decided to ram down culture's throats. The director objects, but doesn't have the courage to say, "You've heard Like a Surgeon, right?" as it would be an offensive question. Instead, he acts as if Rhimes must have something else in mind and makes alternate suggestions. After batting away Lucky Star, Boarderline, and Holiday, Rhimes gives a passionate, American Psycho-esque speech about how Like a Virgin was a turning point for Madonna and the 80s generally. She claims the song is the decade's definitive work.
Hours later, when the director is making the same argument to the writing staff, the head composer, and the cameramen (or whomever), it plays out the same way. Except the story ends with the decision to get Amos Lee to sing the song in his soulful Amos Lee voice and to hype the fact of the cover rather than the disaster of the song choice.
Forced Art
What makes Weird Al a genius is that his entire catalog is a revelation of what pop music looks like to space aliens: Goofy people singing nonsense with heartbreaking sincerity. His work isn't a fun house mirror of pop music, it is an actual mirror of pop music, cartoonishly un-self-conscious to the point where it's unclear whose making fun of whom. Pop music gets a bad rap because it appears to put commerce before art, Weird Al makes fun of the notion that anyone could criticize pop music for not being art by stripping away the pretense that pop music is anything but a silly distraction. He embraces pop music's silliness and amplifies it in a way that's revealing without being openly derisive. Pop music, by definition, ought to be beyond criticism. Given that pop is music people like for no good reason, saying there's no good reason to like it is as redundant as it is naive. 
As the Gen Xers age, just like the Hippies before them, they want to believe their pop music wasn't vapid crap, as if that is somehow more validating or makes their teen years more authentic. But nostalgic ties to pop music are exclusive and emotional to the point of solipsism. They are objectively bad and subjectively sublime. It's something we ought to just learn to live with.
This interplay between soullessness and authenticity is what is troubling about the decision to go with this particular song on this particular show. Since it seems incredibly unlikely that no one had the courage to say, "You're going to play that song in a show about surgeons cuttin' for the very first time?" we have to assume they knew what they were doing. The question then becomes about the choice to use that song.
Given the number, age, and savviness of people involved with the show, it seems likely they were making a comment on the show itself and the weekly nighttime drama generally.
Amos Lee's assignment was to take pointless, meaningless, pop music and use it to render art. Similarly, each week, the staff of Grey's Anatomy is tasked with taking one of the oldest, tiredest, tropes in one of the oldest tiredest genres (the television medical drama) and producing art. What the song choice reveals is that the staff of Grey's Anatomy knows it is on a fool's errand, that nothing new or interesting can be said about their topic using that medium. Instead, they use the opportunity to comment about the uselessness of trying to do something individual in the genre. Just as Weird Al amplified the pointlessness of taking pop music seriously by taking it so seriously as to be parodistic, Grey's Anatomy ratcheted up the emotional content of pointlessness so high, the only song appropriate to push it over the top is a soul cover of a pop song as seen through the lens of a parody. It's a way of admitting that they are taking something vapid and formulaic so earnestly you don't notice.