In most contexts where I've encountered it, a shit-eating grin is a blatantly false grin. It's a grin so wide and so forced that it can't be anything but false. Thus a shit-eating grin, while technically a grin of great magnitude, is sometimes intended to subtly convey the exact opposite of a grin.
In this context the phrase really does make sense; it's just a tricky, very specific sort of sense. The etymology of the expression is best understood with the help of a thought experiment in psychology.
Let's say you're approached by the representative of a major TV news network with the following proposition: his producer is doing a new show called "Who Wants to Embarrass Himself On National TV" wherein contestants do stupid, humiliating, inane things for huge amounts of money.
(Naturally, at this point you interrupt him and point out that the idea is not a new one, and that several such shows already exist. He explains that it doesn't matter; it's a primetime show, and the sole purpose of primetime is to sell advertising. He continues with his spiel.)
The show is hosted by Regis Philbin, and the first hour-long episode will be scatologically themed. They want people stepping in shit; wallowing in shit; smearing shit on their faces; throwing shit at the audience; and, yes, even eating shit. His producer is prepared to pay you twenty million dollars to consume feces in front of a live studio audience and pretend to like it. So what do you say?
You accept, of course. What's that? You say you don't want to? Too bad. Everyone has his price, my friend, and yours is well below $20 million. Also, this is my thought experiment so you really have no choice in the matter.
Come showtime, you find yourself standing on a glitzy Hollywood stage, blinded by hundreds of lights in the rafters. Cameramen record your every nervous harrumph and facial tic from twelve different angles. Regis stands in front of you beaming his own shit-eating grin and reading from the cue cards. Cheesy theme music plays, and a silver platter descends from the catwalks above. On the platter is a dinner plate heaping with steaming fresh turds.
There is a drum roll, a trumpet riff, and Regis hands you a silver spoon. "Chow down!" he says. So what do you do?
You chow down, of course. You put the studio audience out of your mind, forget about Regis, close your eyes, think of everything you're going to buy with twenty million dollars. You scoop a goodly-sized bite of shit into the spoon, raise it to your mouth, gulp, and swallow it down as fast as possible. Because the producers have made it known in no uncertain terms that you must convey a feeling of great joy upon eating the shit, you suppress the horrid shudder, suppress the impulse to gag, and focus on getting it down your gullet as fast as humanly possible.
And the entire time, you're wearing a huge, shit-eating grin.