Well, some American states are extremely hot and dry by UK standards - meaning issues like rot and rust are less of a problem.
And Americans build a lot of detached single-storey houses [1], which mitigates some of the disadvantage of wood: Noisy neighbours? You've got a six-foot-plus air gap between your houses. Fire risk? Escape is trivial when every room has a ground floor window. Rain getting onto the wooden walls? Much reduced by a porch stretching around the entire building. Needs regular repainting? Easy when it's a single-storey building.
Wood is also substantially cheaper in the US than in the UK - so while it might not look like a cheap material from the prices at British wood stockists, Americans who call it a cheap way of building aren't paying those prices!
And Americans build a lot of detached single-storey houses [1], which mitigates some of the disadvantage of wood: Noisy neighbours? You've got a six-foot-plus air gap between your houses. Fire risk? Escape is trivial when every room has a ground floor window. Rain getting onto the wooden walls? Much reduced by a porch stretching around the entire building. Needs regular repainting? Easy when it's a single-storey building.
Wood is also substantially cheaper in the US than in the UK - so while it might not look like a cheap material from the prices at British wood stockists, Americans who call it a cheap way of building aren't paying those prices!
[1] https://goo.gl/maps/de1ZCXtpjS49sSHB7