Anyway the way I learned it is:

* for a given lambda expression, all evaluation orders which reduce to a normal form will reduce to the same normal form.

* if a lambda expression has a normal form, the 'lazy' way (normal order, leftmost-outermost-reduction, call-by-name, call-by-need) will find it.

Actually on re-reading, the article did mention confluence of the untyped lambda calculus, but only went as far as saying that the different evaluation order leads to different termination results, which is not quite as strong as saying the lazy way will find the terminating path if it exists.