The priming line is a small line, typically 1", that connects the sprinkler system to the standpipe system. It has a shutoff valve, check valve, and flow switch, to detect if a hose valve is opened. The standpipe system is thereby pressurized to the same system pressure as the sprinklers, but as soon as a valve is opened, the flow through the 1" priming line can't possibly keep up. As far as the fire department is concerned, the pressure in the standpipe system is not important, it is just a matter of keeping the standpipe system full of water. For a system with a fire pump, the priming line would be supplied by the jockey and fire pumps, or by the city supply (via the bypass line) if the pumps were off-line for some reason.
Interesting point about the sprinkler and standpipe demands. For the building in question, there is no calc back to the hydrant because the water supply is via a break tank. But even for more typical buildings, you don't need to account for use of both sprinklers and standpipes at the same time. The water supply needs to be adequate for the larger of the two (sprinklers plus hose allowance, or standpipe), but it's not expected that the systems meet their respective demands simultaneously. Once the FD is connected to the standpipe system, the sprinklers are no longer responsible for controlling the fire. If the combined demand of the sprinklers, standpipes, and any attack lines the FD is using from outside the building, is in danger of overwhelming the city's supply, they have a big problem.