Agreed. As soon as outflow exceeds inflow though the pressure will drop. It is possible that an increase in supply pressure (which occurs due to a lack of outflow *somewhere*) can overcome the drop and tread back into adequate volume territory.
It is also possible that the increase in pressure won't be sufficient. It's also possible to a have a system where the supply pressure CANNOT REACH the threshold needed to supply the necessary volume at some downstream location.
None of these things is contradictory. There are specifics within the system that matter. As YR (And I think everyone else) has stated: pressure at the sending unit location is not necessarily pressure everywhere. Mostly because of the constant flow issue (because in a static system, Pascal's rule would apply).
