The brine is an inhibitor as Larry notes. Still, it is wise to cool the brine further.
The bacteria most associated with fowl, Campylobacter and Salmonella, are easily controlled by heat, i.e., cooking. Cooking kills the bacteria. Unless the fowl was vac- or injection-brined by the manufacturer (or injected by the consumer) the bacteria in question will be primarily on the surfaces and thus killed quickly. However, even with injected fowl, cooking to a safe internal kills any bacteria that may have been pushed in during injection.
Salmonella and Campylobacter poisoning do not usually come from undercooked fowl (if anything, most people overcook fowl) but from cross-contamination, e.g., removing the bird from its packaging and, say, placing it on a cutting board while preparing the brine, turning on the faucet for water, grabbing apple juice out of the pantry, etc. The cutting board, faucet, pantry door handle, the apple juice lid and jar--anything touched by the bird or by the hands that removed the bird from its packaging is potentially contaminated. It is cross-contamination by direct contact of the bird, its packaging juices (washing fowl is not a good idea), or the hands that handle it and then touch other objects that usually cause the problem.