As I wrote, I've done a few times the other way, from Belgium, where I'm living, to the USA and Canada for repair purposes. Once all the documents are filled and that it's done the same way for the return, it's a hassle free operation.
But bureaucracy meaning a delirious amount of paper, just play their game and everything will be fine.
Also ask the the repair center for an RMA (Return Marchandise Authorisation/Agreement) number with the reason for it stated as this will be the first proof that it is indeed a repair.