Yes. It used to be the job of the home team but that was switched because of complaints about this exact kind of malfunction.
However, we have seen how well the NFL oversees sections of its operations.
So how much of a handle they have over the infrastructure is probably an open question. Remember the Saints were thought to have piped the opposing teams' wireless into the Owner's box for Mickey Loomis to listen too. They investigated it (for some reason the police or Feds were involved I seem to remember) but didn't find anything. But no one thought it was technically impossible.
Its likely that the NFL has rules about how it inspects and operates on Game Day. The Patriots (and everyone else knows this) so its possible for teams to hack it. Problem here is that if the visiting team has a malfunction, they should just turn it off for both teams that half. If possible (and its not the 2nd half) fix it and turn back on after halftime.
Either it all works or its off. If the Steelers are to be believed (I do not take that for granted at all) then the League puts itself in the position of getting played like Klink versus Hogan.