When you access a lounge on a 1-on-1 contractual relationship such as this, AZ pays a fee-per-use to EY each time one of "its" passengers uses the EY lounge (and the other way round as well).

It makes good sense that a carrier allocates just so much to lounge expenses per passenger and lounge-hopping in this instance can easily be controlled.

Needless to say, AZ staff have no obligation to show passengers internal company directives (and indeed I presume that most of their internal communications are proprietary and not for distribution). It would nonetheless be better customer service practice for AZ to make this known in some simple fashion in its lounge access policy.

I really wonder how all of this is tracked and whether it was simply OP's "confession" to violating the policy leading to being caught.