skiesfull..."Continuing with LNAV or GPS when given a specific heading, would be contrary to SOP's"
No pilot would do that. However, if in HDG SEL, and on the directed heading, if the MAP shows you going through the localizer (but the MAP is incorrect because of FMS position error), it is tempting to turn inbound, or in this case to turn to a heading to intercept from the perceived blow-through. It is best to first verify with raw data that you have in fact gone through the localizer before trusting the MAP display in this scenario.
055166k..."From what you say it seems that the aircraft was not complying with an ATC instruction......and therefore carrying out an illegal manoeuvre"
Are you suggesting that the crew was intentionally deviating from an ATC clearance? I have never flown with a pilot who would do that.