Caveat: I know nothing of music theory, so this is an answer based on thinking, not knowing.
Time signatures hold limited information; they're excelent at specifying how many beats there are in a bar, but extremely crude about revealing any other structure in the music. There are obviously loads of structures in a tune, ranging from the beats in a bar through set phrases that have to consist of a certain number of bars, up to the tune itself consisting of a set number of phrases that have a certain relationship (e.g. in a rondo).
The distinguishing feature of compound time is merely that its two lowest levels of structure happen at speeds where we could count either, so we start to think of them as things we should express in a time signature.
The problem is that the same structures can exist in simple-time. A good example is a minuet. Minuets are not waltzes. In a minuet, the first and second bars work together as a unit (and are often echoed in some way by the third and fourth bars, which form a replying unit). The Petzold/Bach minuet in G is a good example; if you sing the first bar, it feels incomplete, while the first two bars together feel more like a unit. In a sense, a minuet is actually compound time, and could happily be written as 6/4, because that's how it's played - it's just slightly slow for people to think of it that way.
From a performance perspective, what matters is that the performer understands the structure, not what they call it. In many ways, the people who wrote Renaissance and Baroque dance suites had the better idea. By specifying "Gigue", "March", "Gavotte", "Sarabande" etc. they told us far more about what to expect than a mere 6/8 could ever convey.
I think what's happening in the original question is that the instructor is taking it that something with a quaver beat (X/8) will be fast. Therefore the next structure up will be obvious. If something is in 3/8, the bars themselves will hold an audible structure that a person could count as a beat, so the listener will hear the two structures going on, exactly as though the music were given the time-signature 6/8, or 9/8 or something, and someone had gone along with an eraser, removing every second (or third) bar-line. There are a lot of assumptions going on here, so I can't honestly say whether I agree or not. It's a bit silly to spend a lot of time deciding whether grey is black or white (though I sympathise with those obliged to do so for the purpose of theory exams).