There are plenty of similar situations that just don't work. And we know for a fact that the Ferengi of the show can't speak a lick of English from Little Green Men (which is a pretty neat episode too).
Watched this last night, coincidentally. Silly but entertaining. Interesting that throughout all of the Ferengi gibberish you still heard the word oomax, which is the one Ferengi word everybody knows.
However, I thought that was a serious undermining of the UT. They suggest that they're placed inside everybody's ear, yet apparently only one person needs it for two way communication. Fixing the one in Quark's ear automatically makes humans capable of understanding his speech. Like plenty of ST tech, it was better when it was left vague and unexplained.
As bad as that is, they've established a few other times that only one side of the conversation needs the universal translator (I can think of examples from at least DS9 and Voyager), so at least it's consistently wrong.
Considering how flawed the tech is to begin with, I'm willing to mostly overlook the issue, given that it's rarely brought up except for times like this when it serves the plot. I agree it was better left vague and unexplained due to the problems, more of a "there's an explanation, but we're not gonna explain it", but I'm not too bothered by it either.
There are bigger problems with the concept of the translator. Translating in real-time simply would not work, given sentence structure variation between languages. And there's the inconsistency of certain words remaining in native language seemingly selectively. And as mentioned earlier, the whole idea of seeing the mouth move in a different language. And the one that bothers me the most is when you see the translator dealing with an entirely new language, where it's a matter of the universal translator hearing the language for just a few minutes and calculating a "translation matrix" and then suddenly it knows the whole language. Again, I know the translator has to move at the speed of plot, but the concept of a translator calculating a formula to instantly recognize new words such as nouns that have never been used before is ridiculous. It could pick up basic syntax and common words quickly, but there's a realistic limit there.
I've always been a tech man when it comes to scifi, so it's a bit of a double edged sword for me when they deal with the universal translator. On one hand, I do prefer to see the tech side acknowledged, and get an idea for the "rules" the show works within, but on the other hand, it does bother me when things aren't internally consistent like that.