Thanks for that link! Although I still think the connection seems reasonable, as Finnish has many loanwords of PIE origin, and the fact that it also appears in Estonian and other Finnic languages (each time with a similar meaning) makes it quite likely that the word has belonged to Finnic/Finnish vocabulary for a long time. Of course, similarities between words (especially short ones) can also be purely coincidental, but still. Derivations don't always follow 'the rules', either, and commonly used words in particular are highly resistant to change.

I was doing a little more research, and now I found out that long ago, the PIE 'med' ended up in the Uralic tongues - it was lost in Finnish but continues to exist in Estonian, Hungarian and all of the smaller languages, all with the meaning of 'honey'. Our ancestors must have really, really liked their honey.

(I'll see if I can take a picture of some fungi to offset the whole discussion about honey.)