operator new and implicit creation of objects

This hinges on whether a "name" means unqualified or fully qualified. Per [basic.pre]/3 it is unqualified:

A name is ...

(3.3) — an operator-function-id ... [or some other things]

Where:

operator-function-id:
        operator operator

operator: one of
        new ...

So member operator new/operator new[] are also included in this.