Quite untrue. A 3 city HA rush will snowball the game much earlier. The only time I think you even need Cuirs/Cannons is on Deity. Anything Immortal and below you can simply LoL Knight pwnage and turn off research around CS.Of course not. The idea is to get the game to a strong position whether you want to go for Construction or Engineering or Cuirs/Cannons or whatever. And the mechanics of the game make that, in this particular case, having 5 cities on T50 is better than having 3 cities on T50, even if the latter saves you some forests.
And this goes out to anyone following this thread, take a look at any HoF or non HoF games (space, conquest, Dom) that have the earliest finish date, regardless of level. Virtually every game has very, very, VERY few "initial" settled cities. Even if you have lot's of land you "could" settle it's usually the best choice to stay small and start the War Machine snowball as soon as possible. This coincides with my own HoF and Civ4 experience too.
Theory craft and personal play style are w/out a doubt one of the great attributes of Civilization 4 but having said that, the results found in the saves are the proof in the pudding (until new styles and theorycraft post better results).