Valmai correctly identified the song I was thinking of.

The original form, which is easy to find in anthologies nowadays, is:

Westron wynde, when wyll thow blow,
the smalle rayne downe can Rayne
Chryst yf my love were in my armys
and I yn my bed a gayne.

It was published in that form, and with musical notation, in Ancient Songs: from the Time of King Henry the Third, to the Revolution edited by Joseph Ritson (London: J. Johnson, 1790), page lv.

However, when the same song appeared in Popular Music of the Olden Time by William Chappell (London: Cramer, Beale & Chappell, 1859), page 58, it was changed to:

Westron wynde when wyll thou blow?
The smalle rain downe 'doth' rayne;
'Oh!' if my love were in my armys,
'Or' I in my bed agayne.

Note that he uses single quotes (inverted commas) as a subtle admission that he had changed something.

But maybe this doesn't fit within the scope of your thesis, since these scholars had not collected the song in the wild, so to speak, but had found it in an old manuscript from the era of Henry VIII.