I don't think that's true at all. The beauty of a 433/4321/diamond is its flexibility. Here are a couple of ways we could do it:
Anderson Carrick Cleverley
-------Rooney
Valencia RVP-----------
...with Rooney in a totally free role. He can stay in the hole, he can push forwards to become a second striker, he can push wide to provide width. If he's in the hole and we need more width on the left, Cleverley can pull out wider. Or Evra can push up and be more of a wingback, safe in the knowledge that a 3-man midfield gives him much more defensive cover.
Anderson Carrick Cleverley
Kagawa Rooney
RVP
In this one there are so many bodies in midfield that the fullbacks will have massive licence to come forward. And again, any of Anderson, Cleverley, Rooney or Kagawa can provide width if needed. Just because no-one is in a winger's position on the team sheet doesn't mean there's no width available.
Carrick
Anderson Cleverley
Rooney
RVP Hernandez
As above, really. Although this one probably doesn't lend itself to width. But then that's not always a bad thing.
If you want to play Nani, swap him for Valencia in the first or Kagawa in the second. Either formation would suit him.