Well, the store just said "authorized" but not "ASUS authorized"? Maybe this is a 3rd party the store trusts to do repair work but it's not actually an ASUS facility? Not sure.
The good news is that a faulty connection is generally very easy to fix. They either need to resolder a connection in the ear cup or replace the cord. So it doesn't require a special facility. However I would check it thoroughly when you get it back. Shake the headset and flex the cable around to make sure there aren't any weak spots.
A bus station is where a bus stops. A train station is where a train stops. On my desk, I have a work station…