I do not have a solution per se' but will tell what I know based on my exerience with this same error.
Used my son's Ipad mini and never got this error ever. His Ipad mini had tunes on it bought via Itunes. So he had some songs on it and I am just pointing that fact out.
I got a new Iphone, had no itunes songs myself and it always got this same error you mentioned, even so the Amplifi App would work but no tunes to tone match against. Log in on Iphone, get this error then I think I said OK and then the Amplifi App worked despite it. I had MyTones to select from as I started first using my sons Ipad mini which did tone match given it had tunes on it.
Didn't seem to be caused by the Iphone's bluetooth or wifi being off and I always had wifi turned on before launching Amplifi app.
But I did these two things and not sure which may have fixed it as doesn't occur for me any longer on the Iphone.
1) bought one itunes song. 2) enabled the Amplifi App to use cellular data.
If I had to say which fixed it probably having an Itunes song on the Iphone.
I don't get the error any more on the Iphone and never ever got it on my sons Ipad mini. My son has his own Itunes account for his Ipad mini.
I would think Line 6 support would know exactly what is causing this, perhaps open a support issue with Line 6.
If you have no tunes buy at least one and see if that fixes this.