rokeby, the picture is a good illustration of what I had described. The dc from the solar panels goes to the inverter which converts it into ac in synchronization with the grid. Where that current goes depends on the loads in your house: if the house is consuming less than what is being generated by the panels (through the inverter), then the excess goes out of the house into the grid. If the house consumes more than is being generated, then the current flows from the grid to the house, adding to what the PV system produces. Technically, your drawing does not specifically show the PV-originated electricity being used directly, but does shows it complementing the grid-originated electricity.
There are other schemes for storing electricity, batteries being most common. I have such a backup system whereby the solar panels drive a battery charger which charges and maintains a battery bank. If the grid goes down, I simply use the dc from this battery bank to drive an inverter which puts out ac that is usable by my home's lights and appliances (and iMiEV charger). How much power this system can put out and for how long it does this is simply dictated by how big a backup battery and inverter I want to spend $$ on.
You may have heard the expression V2G (Vehicle-to-Grid), where the electric car's battery is used as the source of energy which gets fed into the grid. This concept can provide the utility with a much-needed buffer to handle peak loads.
Allied to this concept I can, in a matter of a few minutes, easily hook up some battery chargers to my other electric cars to feed my backup battery bank to keep me happily living "off-grid" should we lose power again like we did for a week after the Loma Prieta earthquake. Hopefully my solar panels and garage survive the earthquake so I can do this...
Regarding what the electric company does for payback - the schemes and rate structures vary from state-to-state. For example, in my service area in California, my PV system can be used to bring my electricity bill down to zero at the same rate as would have been charged me. Don't get me started on issues with how that works in real life...