Well... I have returned, but unfortunately the store doesn't have a return policy.
At least I managed to convince them that there was a problem. They will bring another one that they have in a different store then I can test. It seems it is the beginning of a long soap-opera. :(
The one I got is the JTV-89F BTW.
I'm happy with the general "quality" of the guitar with the magnetic caps... it sounds great... The only issue is this annoying issue with piezzo, it makes impossible to use drop D, drop C...
I wish I had seen this thread before buy it. I'm really disappointed with Line 6 ignoring the problem...