No. In the real would "anything" is not possible, and that it is an odd statement to make. It's not at all uncommon for me to see or be a part of a problem solving process that at some point includes a statement like "given the constraints we're under, there is no current solution." Now the next stage might be something like "We can eliminate one constraint by doing X, which will cost Y dollars" etc. So in the MU problem one might say "Given the string transformation rules, MI cannot become MU. However, if we added rule X, then such a transformation would become possible."

All of which is besides the point: "Puzzle" and "Riddle" are pretty much interchangeable. They appear as synonyms for each other in thesauri; "riddle" is given as one of multiple definitions for "puzzle" in wiktionary. Many sources treat "riddle" as a kind of "puzzle". The degree to which riddle might be more appropriate in a given context relies on a few factors, for example riddles often tend towards more verbal basis, spoken or written. A puzzle is the broader category and can include things like physical object such as a 500-piece jigsaw puzzle. But any difference is still only that of broader category and specific type. Either term is valid here.

So stating "It's not a puzzle, it's a riddle" is indeed splitting hairs, or simply not knowing the nuances of the actual definitions of those words. The OP of that comment appeared to be doing so with the implication that the whole problem was somehow unfair as a result. I cry foul on that assertion for the reasons stated.