You only need to disconnect battery for about 1-2 minutes, when this happens to me.
Happened twice, had radio replaced once.
They have to PROVE your aftermarket equipment caused it. You just keep on saying you don't understand how it affected the radio until they explain it or give it up, especially if you know what you're talking about, let them walk themselves into being a fool.
Chances are they're full of ****, and just trying to get an extra $ out of you.
I've had it happen, but I wouldn't pay like 90 $ an hour for them to fix something (a light out in the dash of my tundra). I just shook my head, and told them "Just change the oil then" or whatever routine thing i was in for.
But just un hook that negative, it's a PITA, but it will reboot itself.
With mine they didn't even look at it, just replaced it. Was it MP3 discs? that's what it was with mine.
This has happened a few times before, but I've not seen it for a while. It does take a while to get your discs back, and someone told me theirs were scratched when they got em back in the mail. Maybe used burn discs if you're worried about it.