Is Billy in jail?
Yeah but that whole oozing and leaking nastiness makes him not entiely appropriate for sitting it a cell unattended.
That seems true, although, and this has for sure been said before, is the jail cell the best place to keep Naido safe? And, since we're being logical, wouldn't they have taken her to the hospital to see about her eyes and to test for exposure to the elements after surviving naked in the woods for an unspecified amount of time?
They are following Andy's lead, since he has special knowledge now, and knows she isn't of our world.