i don't know about Crouching Tiger, Hidden Dragon but many foreign movies now, have the actors "say" the lines in english.. and one or two frames (especially close ups) are added to film for foriegn distribution.

then, when the lines are dubbed.. the mouth movements "work" -- the actors don't have to get the lines perfect to have the dubbing look good.. so it doesn't matter if theys say fright or flight.. the shape of the mouth is the same.. and the professional who dub just work at getting the word right, and matched to the the actors lines..

since many film earn more in foreign distrubution than they do in home markets, its a cost effective decision-- some time there will be "takes" in several languages.