I chose the two scenarios I did to illustrate that "frames per second" is clearly not meant to be measured in terms of times the display refreshed, but rather in terms of times content was actually rendered by the game engine.

In my opinion it is quite difficult to provide a definition of "fps" that somehow makes 45-fps-native-with-frame-doubling be counted as 90 but doesn't also make either of the ludicrous examples I presented be counted as 90.