> The person in the cleanroom knows what the output is supposed to be, so how clean is the cleanroom really?

Very, this is the entire point. If you only know an input/output mapping, then you don't know the internals of the original product. Your implementation is "clean" wrt that potentially proprietary knowledge. You use the two-room approach (one team in a dirty room seeing potentially proprietary information, one in the cleanroom with only the spec) to ensure that segregation of knowledge for your future legal defense. This lets you make the case, in court, that any duplication from the original to the "clone" (or whatever) product is just coincidental, or the consequence of standard design choices.

If you don't use this approach, you don't have that cover, and you have essentially no defense if copying is found.

Remember, the main point of this is the legal defense.