Oil pumps again...

Well, if the cam is riding in the bearings then what do you think? And if the rockers are grabbing the shafts, what do you think?
First of all, the actual question was, "does a HV / HP use more engine HP"?.
Not "will a HV / HP pump free up HP by masking a mechanical issue in the engine".. so your post above is irrelevant..

That's why I said earlier about bench testing the pump, because the conditions are controlled and repeatable without having to factor in other elements/ issues from an engine that may skew the results..

Obviously if your seeing an increase in HP when adding more load via a HP / HV pump, then it's not some magic in the pump. Something else is going on..Maybe it's in the engine, maybe it's the test procedure, etc..
What do you do next??? Identify the actual issue? Fix/modify that issue and then reduce pump pressure/drag to free up even more HP, than just the band aid pump solution with sky high running pressures?? I'll let you work that one out on your own..
So obviously saying it's an "old wives tail" and then applying it to every situation is just stupid....and it's why you're a pudnocker.