Maw doesn't fire off of an Archangel accessed in a server (R&D/HQ) if the Archangel bounces Maw. After debating about this on slack, I asked Jako to roll me through his interpretation of it. Basically, Maw is conditional on the access ending (it's referring to the overall access of 4.5.X; it cannot be referring to the access event at 4.5.1 of normal "on access" effects, because it needs info from 4.5.2). Since Maw will have bounced back to hand before the access ends, Maw could not fire.
As another example, Maw does fire in the case of an accessed agenda being hosted on Film Critic; all that matters is that it is the first time that an access occurs without scoring or trashing occurring.
Also note that, if the trash is replaced (IE: Salsette Slums), it is still considered to have been trashed, and thus Maw will not trigger (and can still be triggered off of later accesses). This might seem counter-intuitive given film critic, but SS replaces the trash, whereas Film Critic merely prevents the scoring from happening (pre-empt's it).