A deeper discussion is in Wikipedia under "musica ficta", where it is explained in lots of words that basically a good musician either knows the appropriate "inflection" or makes it up as s/he goes along.
Remember as well the notes played "in the olden days" were in modal "scales" probably using just intervals pitched from whatever "A" they were using, and so cannot be reproduced easily using instruments set up in equal temperament.
It is possible, though, that this wouldn't be noticed after a few pints of ale.