Having worked in AZ for 7 years (although I since have moved elsewhere) perhaps I can shed some light on the issue... the AZ "General Basic" (ie Operations Manual) states that off-duty AZ crew SHALL introduce themselves to the Captain. This is so the operating flight crew know that there are extra crewmembers available should the need arise (unruly pax, pilot incapacitation etc).
Of course this cannot apply to crew from other airlines, but by extension AZ flight crews still like to know when you're on board, and generally appreciate if you introduce yourselves (I even remember some captains getting offended when they didn't, just like lenzuolo says...).
Thus when you greet the purser, introduce yourself as a pilot from airline XYZ and then ask "posso salutare i colleghi?" indicating the cockpit. The purser will then ask the captain if you can come in and most times you will be greeted warmly.
It is NOT assumed you are doing this to get an upgrade. Having said that, until very recently, 9 times out of 10 you would have indeed been invited to sit in business (or even the flight deck on occasion). Recently however all AZ flight crew have been issued with a stern written warning to immediately cease this convivial practice... (much to my dismay, as I use my old airline regularly to commute)
If you have noticed a change in attitude recently, it's because the morale in AZ has hit rock-bottom
... nothing to do with you.
MD
PS Can't speak for AirOne but suspect it must be the same...