Partially correct, but... IMO, if that were the problem (bad water
pump) 2 things would happen differently:  The engine would overheat
and it would *not* produce heat at higher rpms.

My guess would be the *auxillary* water pump is bad.  That's the
little electric affair that is used to mnove heated coolant through
the heater core.  When rpms are up the main water pumo (the one that
was mentioned as having a plastic impeller) builds up enough pressure
to get some coolant through the core, but at idle there is not enough
(hence the need for the electric one).

Now, even having said that, if you have never replaced your main water
pump before I would do so as they will self destruct (as zz said -
junk) and may well cause engine damage when it does if you don't catch
it in time.

-Fred W