The cases where the sword was signed by a student or signed by someone who knew how to sign (as many early smiths were illiterate or someone else was just a good carver) is not considered gimei.
It is very expensive to remove a false mei from a blade. Only a highly skilled polisher can do this correctly. The mei is carved/cut out, and the tang reshaped and repatinated.
Darcy was right in his analogy. Look at it this way. Some guy finds an old unsigned impressionist painting. He then decides to sign the painting "monet" and tries to sell it for the millions an original monet would fetch. Then an experienced art dealer examines this painting and realises it's not a Monet but really an unsigned Van Gogh! The value of the painting is diminished because of the "blemish." No museum or self respecting art collector would hang up Van Gogh painting signed Monet. Most would try and restore it to its original state.
with a blade you can correct this situation. in the above case, it would be wise and responsible to remove the gimei. In other cases, that "monet" might turn out to be made by a 2nd year art student at your community college. In this case, it is not necessary or advisable to remove the mei.
Just my 2 cents. As always, someone correct me if I'm wrong.
mike