Languages and how they work for a DM

He could be right that languages can be learned as they progress, and leave his language slots open for that eventuality, but it wouldn't make sense to fill any of them ahead of time if you could just learn them instantly. My approach has always been to say that those language slots mean they can learn that many languages with sufficient exposure, and even do so fairly quickly (as in learning the basics of a language similar to their own in under a month with dedicated study). You have to use common sense as you limit those new, incoming languages (they have a right to them in the rules), but certainly they should need to visit a speaker of the language or a library or both and put in some in-world time to learn the language before being able to solve you puzzle. If they have no familiarity with the language, no roll should be high enough to read it, but maybe high enough to guess a bit with cryptography and general intelligence. They certainly wouldn't know any of the language beyond what they saw on the puzzle itself.

In my campaign, even elves who speak elvish natively will still run into local words and dialects that they can guess at from the roots or are hard to understand. By the same token, a lizardfolk might be able to recognize cognates in the kobold tongue and communicate pretty well, depending on intelligence.