Nope, not true for anything other than a smallsword (the closest thing to a real combat version of a fencing foil).
A single-handed, double-edged cutting sword should balance about 3-7 inches from where the top of your hand is when you're holding it. Closer to 3 for something you'd use more for cut and thrust, closer to 7 for a dedicated cutting sword for use from horseback.
A hand-and-a-half or light two-handed sword should balance in the same range, but are best served with a closer point of balance.
A large two-handed sword should balance no more than about 8 inches from your top hand.
A short sword/long dagger intended for stabbing/thrusting should balance right where the hilt meets the grip.
A rapier should balance between about where the rings furthest from the grip reach, to about 2 inches beyond them.
I think a katana is supposed to balance right at the tsuba (the guard), but I could be wrong.
Weight is a very different matter, however; a one-handed sword, under almost any circumstances, shouldn't weight more than about 3.5 pounds, and that's for either a really heavy chopper or an exceptionally long and balanced rapier. 2.5 is more like it. A hand-and-a-half sword shouldn't weigh more than 4 pounds, under any circumstances; 3 is more like average. 8 pounds is heavy for a greatsword, 5 pounds is on the high end of average.
So, that's just what a guy who's been studying *swords for six years has to say. I'm not saying I'm an expert or anything, but I'm basing those numbers on the documented stats of surviving antiques, as well as the modern-made replicas I've seen, handled, and cut with.
*(though not swordsmanship; don't try to ask me how to counter Pflung while in Ochs)