Normally, as per ST rule, you were entitled to go to the AZ lounge for sure. When the airline you are flying has a lounge or a contract with a specific lounge (e.g. in your case the Montale lounge when flying SV), it can happen that another ST lounge is denying you access because of being too crowded and needing to keep some space for their own pax & Elites. There has been such reports in the FB forum at JFK T1 where AZ and KE pax prefers to go to the AF lounge rather than using AZ or KE lounge and they've been denied access in the evening for the reason I mentioned.
But in your case, reading you, I have the feeling that it was a no for the pleasure to tell you no and "we don't care about ST" which I believe is typical from AZ having one foot in ST and another one outside.

As I said in another thread yesterday in the FB forum, IMO there are too many lounge access problems in ST (we get more and more reports like your) and you should complain to AF/KL (as a FB member). They need to work on this at the alliance level.