even though this makes plenty of sense taken on its own, it wouldn't do much to explain her speaking English there. I'd think the Romulans would have caught the English (or Betazoid speech).
We don't know that the Romulans were hearing anything but Romulan coming out of their UTs. It was the TV audience that was hearing English.
Maybe the reason Troi was chosen as the spy was that she already knew some Romulan?
I was addressing this as an either-or between the two possibilities. I can't play with the middle ground there because it is too much of a stretch to suggest that the Universal Translator could somehow transparently correct her incomplete knowledge of the language they'd expect her to be speaking (I can't imagine it could translate Romulan into "better Romulan," especially unnoticed.)
If she knew it then that's that and the UT doesn't have to be involved, but as I said, it seemed like a big thing not to mention that Troi knew the language. I do think it is to some extent implausible that Troi would know much, if any, Romulan spoken language when the Romulans had evidently been out of contact with the Federation her entire adult life prior to "The Neutral Zone."
If the UT was translating the English she was speaking into Romulan, this is anything but an explanation. I'm not referring to what they hear "coming out of their UTs," but the actual English she would be speaking. How could it not be obvious that she was using a translation machine? I will cut Trek a break on some stuff and enjoy rationalizing oddities, but I don't think I am willing to entertain the concept that the Universal Translator is not only an amazing translator that knows what people are trying to say and makes it understandable, but is also a kind of force field/holoprojector that somehow reaches into the throats of speakers and selectively jams the sounds that are actually being made by the speakers and generates its own and then creates the illusion that its sounds are sourced from the speaker, and not only does so in real time but sometimes by projecting ahead and guessing at words that are yet to be spoken! Even if such a device did somehow exist in Trek, I have to think that military personnel on a warship transporting an intelligence agent on a secret mission would be the last to allow themselves to be fooled by it.
It seems almost as unlikely that most astronauts in the Federation have heavy-duty cybernetic brain implants or whatever that alter their perceptions while translating.
I don't think we are supposed to interpret the fact that English is typically spoken on the show as a direct simulation of what would be experienced in that sci-fi universe; we have to interpret the functioning of the UT in some semi-realistic way that still allows it to function smoothly enough to permit the situations in Trek. Usually this is quite possible and I don't have any problems with it (for example, I imagine the hails between aliens that have never met before contain some sort of computer Rosetta Stone kind of business based on prime numbers or some easy point of entry, and that the computers can learn enough from these initial transmissions to allow dialogue.) The "infiltration" episodes are one example from a very short list of things on Trek that really give me pause.
Wasn't there some whatnot about "brain waves" being part of how the UT worked in TOS? Could some necessary and useful commonality in brain waves exist between different species? I try really hard to find some rationalization hiding somewhere in that.
Hey, maybe while she was knocked out a Reman came in and mentally force-fed Troi a bunch of Romulan words!
I meant this as a joke, but upon reflection, maybe it is the best I can do. Telepathy in Trek is not especially well explained or scientifically plausible, but at least it's established in the setting.