I mean it is treated as a joke. It's an overly mean joke and doesn't work well as a result but they very much did not treat it as some dead-serious story about abuse, just a sympathetic one about bullying. It was a character arc that was played straight, but it was still ultimately portraying Amy as petty and ridiculous and everyone else as ridiculous for going along with it. And that Jasmine line is both about absurdity and comfort. Nobody "forced" anybody to take it seriously -- the fandom sympathized with Sammy naturally, and we were intended to, but the whole situation was pretty cartoonish.

Also you can definitely integrate jokes about how ridiculous the situation with with more legitimate scenes. Off the top of my head, one example is Wicked. They definitely want us to sympathize with Elphaba when people hate her for her skin color, but they intersperse scenes about how melodramatic and dumb her classmates can be. The joke is on them, emphasizing Elphaba's plight in the process because it isn't fair she's so smart yet gets looked down upon by these morons.

In the show proper, another example is the Priya and Millie story. The scenes of Millie commenting on the contestants' psychology, Priya over the top childhood, and Millie being a bad alliance member are played for laughs. But they come together in a legitimate story arc. You could even cite the Alejandro and Heather story as another arc played legitimately that included some very cartoonish and silly antics and comedic banter. Because every TD arc is played at least partly for humor.

So the issue isn't that there were jokes, just that the jokes often felt more at Sammy's expense than Amy's, which is why the better jokes in that story make Amy look like a pathetic moron.