That is pretty bizarre. The parking lights are supplied via the
#38 fuse which is supplied by the taillight relay and the taillight relay is switched on by the headlight switch. The
#38 fuse also supplies all those other lights, so if the parking lights are getting power from the
#38 fuse those other lights pretty much have to be on.
Pull the
#38 fuse and then turn the key to the on position and (with the headlight switch off - although with the fuse out it shouldn't matter) see if the parking lights go out. If the parking lights do not go out, then you have an alternate circuit keeping the parking lights powered up. This could be some kind of bizarre sneak circuit (unlikely if the other lights are not lighting up) or somebody has wired in a constant illumination circuit for the parking lights.
Did you import the vehicle or was it imported by somebody else? As an observation, when the vehicle goes through the RIV process I believe it is a Federal (not provincial) requirement for the car to be retrofitted with DRLs. The details of the process are now a bit fuzzy for me; but, as I recall the vehicle has to be inspected and somebody has to sign off that it has been brought into compliance with federal standards before you get the RIV sticker which is supposed to be attached to the vehicle. I am not going to tell you about your vehicle; but, if it went through the RIV process (pretty hard not to if you want to register it) then it should have a DRL install. What might have happened is that if the DRL wiring was done poorly, it may have stopped working which would cause it to revert to the way all US models worked. Perhaps if you hit a bump a bad connection was re established and you are back to having functioning DRLs. The only way to confirm this is to inspect the wiring to the parking lights and see if there is some non Honda wiring down there.