I don't understand why you say that that either device (the furnace in particular) would pull air in. Certainly the HRV will, but when that is off the inlet duct should automatically be dampered off. At least that's the way mine works (a Lifebreath 195ECM). The furnace fan should just circulate air within the house, unless there is an outside air inlet connected to it.

A lot of how you should run your system depends on the nature of the house, mainly how tight it is, and on how the air distribution ductwork is set up. An HRV usually is installed to ensure adequate ventilation in a very tight house. In such a house, the HRV indeed should be on all the time, or nearly so, at a low flow rate matched to the proper ventilation rate as specified by ASHRAE 62.2 (or Canadian equivalent).

In my system, the HRV dumps the conditioned incoming air into the return duct of the heat pump. There are three zones, and when none is calling for heating or cooling all zone dampers are open, so that air fed in by the HRV is distributed through the house. The heat pump fan does not have to be on to move the air.

If you have windows open in the summer, then yes the HRV might as well be off to save power. Otherwise it can be left on to provide fresh air if the house is tight, because you won't get much ventilation at all from leakage in summer if the windows are closed. Furthermore, human occupancy produces a fair amount of moisture (cooking, showers, plants, breathing). Bringing in humid outside air will contribute to the humidity in the house, but without ventilation the air in a tight house could get humid just from human activity. A dehumidifier could be a solution if there is no AC installed.

Thanks for the reply DickRNH.
I guess I just made the assumption that the furnace fan would pull air from outside through HRV even with HRV off. I still got alot to learn how this system works. I seem to have a lot of moisture in the basement air. I mean it's not dripping but 55% humidity or more. I thought maybe the HRV was pulling the humid air in. I'll try some experimenting with HRV and will maybe invest in a better dehumidifier.
Thanks for your help.

Humidity in the basement could be from the ground, especially if the foundation walls are not insulated and there is no insulation and vapor barrier under the slab. Concrete is very porous. Even if the surface does not look damp, that could be just due to evaporation as fast as it diffuses through from the soil.

You can test this by taping a sheet of polyethylene perhaps 3 feet square to the concrete surface. After a day or so, if you see condensation under the surface of the poly, then you have damp concrete. Even if there is little moisture coming in from the surrounding soil, you could be getting condensation of humidity at times from humid summer air against the cold surface of the concrete.

Given where you are, if the concrete walls are not insulated then you ought to do so. Rigid foam board 2" thick can be glued (PL-300) or fastened mechanically to the walls, then covered with sheetrock for ignition protection. If you have electrical outlets along the walls, then you could erect a framed wall of 2x4s on the flat against the foam sheets, use shallow "pancake" electrical boxes for the outlets, then cover the frame with sheetrock. A good reference for information on stuff like this is at www.buildingscience.com.