Well, that is not the reason.
As I recall right the Cirrus aircraft are not JAA approved as a whole.
If I remember well it has something to do with the stall tests.

And the same works the other way, if a part or plane is JAA approved it
is not automatically FAA approved so no change of using it in the US.

And this is not only related to aircraft(parts).
Buy a used or classic car in the US and try to have it legaly road
going here you have to change at least the seat belts and head- and
tail lights to CE standards.
And then you are lucky, wait if something enviromental pops up :-(
Export a car to the US and you have the same trouble again.

And there are more regions in the world with their own standards and
rules.
It sometimes drives one mad.

-Kees