It means the black wire is indeed hot. Are BOTH switches (OH light and switched outlet) receiving power? Typically one is daisy chained to the other.
So, take one room (which is probably representative of them all). The power comes in and goes to the double switch on the wall. The first switch controls the ceiling light. The power is there but the light won't work. (I haven't checked the ceiling light to see if the power is getting through to it, but see below). The power then goes from that switch to the switch next to it which controls the switched outlet. This switch has red and black wires connected to it. The black has power (it's just come from the switch next to it) and so does the red when the switch is turned on - as you would expect.
I then check the switched outlet to which it's attached. It has white wires one side and red the other. The white wires have power and the red has power when the switch is turned on - no power when the switch is off. Yet, if I plug something into that outlet it won't work. I've tried lamps and a food mixer which I know work elsewhere. How can that be?????
Any advice/thoughts appreciated. I feel there might be a simple solution to all this.