We are descendants of the same John King Fairfield Sharp and I too think this is very likely, in some way or another. We know that his father Gilbert P Sharp was born in Ernestown... which I've heard had other Sharps, as did Bath and Adolphustown.
It stands to reason that since that family stuck pretty close to the Prince Edward/Hastings counties almost their entire lives (Frankford, Picton, Sidney, Tweed) and since this is a family that tends to honour family members by using their last names as middle names, there was a Fairfield among us at one point.
JKF Sharp's daughter Alice named her son Walter Fairfield. And Ripley is another family name that pops up as a middle name every generation or so. For this reason I also think Amos Hollingshead Hill was named after a relative that had the last name Hollingshead. It seems too odd otherwise. And it's just too much of a coincidence that there were other Hollingsheads residing near them in the 1871 census.
It would be great if we could uncover that missing link.