This INS thing is a bit of a red herring. ContactTower seemed to be saying his GPS might upset things. Perhaps another GPS might be the most prone. That GPS might show some misreading which could corrupt the FMS's opinion of where it was. That sequence of events is unlikely. GPS is digital so you can't 'bend' the reading, and wherever navigation information is blended there is going to be some process which rejects 'odd' inputs. The loss of a valid GPS input is something that would be designed for.