OK. I am looking at http://www.thesession.org/tunes/display/57 - Old John's Jig. On that website the ABC for the tune is given as follows:-

X: 1
T: Old John's
M: 6/8
L: 1/8
R: jig
K: Ador
|:cAA cAA|GEE GAB|cAA cAA|Add ded|
cAA cAA|GEE GAB|cde ged|cAA A3:|
efg eaa|ged cAA|efg eaa|bag a3|
efg eaa|ged cAA|cde ged|cAA A3:|

No "F" note in the A section, but three in the B section. We can see that Dick has correctly described the tune as being in "A Dorian". Now if we go from the "ABC" tab on that web page to the "Sheet Music" tab, we see the notated tune (which sadly can't be reproduced here) written out with a key of one sharp ( as if it were in in G major or E minor) so that the one sharpened note is the "F" and the sheet music does not indicate the need for an F natural.

So how does Dick answer Greg's comment that I think almost any use of an Fmajor might jar and confuse the ear when there seems to be no F natural in the tune. In which bars would Dick introduce an F major chord?