Wrong. As sfb suggests, when pushing hard you have far less than your whole bodyweight resting on your saddle.
I'm aware of that, but that's not the situation I used it in, maybe I didn't explain what I meant properly. It is possible to sit on the seat and pedal hard without reducing your force on the saddle, you cause do so by pulling up on the upstroke to match your downstroke. The point was to remove gravity effects from the build-up so it was a little more clear, unfortunately it made it a little less clear.
Any net force in any direction from the two cranks gives you an increase or decrease in apparent saddle reaction force. As long as you can match the downstroke force with your upstroke force you can hold your body still wrt the cranks. If your net force goes positive (pushing harder than pulling) you'll start to unweight your body off the saddle, therefore the maximum net force you can apply is whatever your upstroke can apply+force from your body weight. After that you have nothing holding you down anymore, unless you're also able to stop your rotation about the handlebars, but I'd expect that your grip isnt that strong.
I suspect the reason they say (in that link provided) that net efficiency goes down is that the upstroke is less mechanically efficient (due to the position, size etc of the muscle and limb) and so drags down the overall efficiency even if it shares the loads. But that's in sub-maximal case, in the maximal case where your push muscles are working at full tilt, bringing in a little help from the pull muscles may well extend your range.
