Worth noting that rhyming clues are mentioned in the rulebook as an optional rule you can play with.
So I had written up this whole thing about how this is an example of clearly cheating, because unless you are playing a game where bluffing is built into the mechanics, you can't ever "hope to get away" with doing something that isn't normally allowed.
But then I double checked the Codenames rulebook, and... it seems that those people are technically correct.
If a spymaster gives an invalid clue, the
team's turn ends immediately. As an additional
penalty, the other team's spymaster may cover
one of his or her words with an agent card
before giving the next clue.
But if no one notices that a clue is invalid, it
counts as valid.
So they are playing within the rules when they try to give an invalid clue... if it were completely outside of the rules, then you wouldn't have a penalty for it; games don't generally need to give rules for what to do when you don't do what the rules tell you to do.
That being said, that sounds like adding a very un-fun meta game on top of the rest of Codenames, and it's not a way that I would want to play, nor would I want to play with people who do play that way.
So really, it's just something that needs to be discussed and agreed upon at the start. They aren't cheating when they do it, but it doesn't seem like the rules are intending for that to be used as part of a strategy. Plus, it's an extremely risky strategy anyway; you should be getting caught much more often than not, and the penalty for getting caught is really bad.
*Edit* I just noticed that you referred to "exploiting a rule", so you already knew what I quoted. I agree with you, the rule seems to be intended to deal with accidents; not to be used as a strategy. Again, I wouldn't allow such a thing in my games.
Puerto Rico actually has the same problem; the rule book says how to handle the situation when you later realize that you forgot to load the ship at the end of the Mayor phase. This opens the door for people to purposefully "forget" because they want the alternate outcome. Such rules are bad and shouldn't be in rulebooks. The proper rule for "what do I do when the rule wasn't followed" should always be up to the people playing the game to handle as best they can without screwing things up.