Knowing very very little about battery technology I wouldn't expect an interruption when starting to charge a pass-through power bank either. I'd expect charge controllers to handle this seamlessly, like the ones I get on those microcontrollers that support batteries out of the box (which are dirt cheap too), or the one in my laptop, or the one in pretty much all other battery-powered devices; those don't switch off when connecting/disconnecting to/from mains power. If that's so well-understood, why would a decent power bank not do this as well?
Actually, my big Anker 521 (256Wh) does provide pretty much uninterrupted power when connecting/disconnecting to/from mains, though it did switch off randomly once after a few days.
the author says this as if the two are easily confused, when its him that makes the association in the first place. why would you assume this at all?