Cool. I have never seen the "fair catch kick" rule evoked either. You know, at the end of the quarter if a player calls a fiar catch with no time left, the team can elect to get a free kick.
The Dallas Cowbows actually used that rule once back in the 1970's.
I'm no rules expert but, I believe the 'fair catch kick' is other than described. I believe it goes like this. If a fair catch is made of a 'free kick', then the receiving team can also have a free kick at the point of the fair catch. That free kick can result in a field goal. Whether this occurs at the end of a quarter is irrelevant.