From an engineering perspective, (and I'm sure the Water Department folks will confirm) its probably better to say that water delivery systems are "designed" to support fire protection. A fire has a greater demand on the system than a block of houses. You can always get water from a well, but you can't put out a fire with one.
From a business perspective, the water department serves the fresh water consumer - because they pay the bills. The fire department does not. Money talks...
For the OP - Your first assumption is probably correct. The high head water tank in your neighborhood is your local only reservoir of fresh water for drinking and maybe firefighting. In the event that a tsunami inundated the water filtration or purification plant near the shore, the water in that tank would be rationed by the water department - otherwise they would run out of supply very quickly and have a worse situation on their hands. (In an extreme circumstance, they could keep it locked off and truck water from it to other parts of their service area and not just your neighborhood.)
I would also expect that the fire department in your area would have a hot line to the water department to restore pressure in the event of a major fire. Otherwise they would fight smaller fires with the supply on their tanker trucks and refill directly at the water tank.
NUTTSGT's advice is what you should follow. Fill jugs and the bathtubs in case water is rationed. In a rationing situation, the fire department will get first dibs on what's in the water tanks until bottled water supplies are at a dangerous level - particularly if you live in a dry area. (FEMA stockpiles water for emergencies like this.) You can drink water from a bottle but you can't put fires out with them.
Someday... as the need to conserve and recycle water increases, many of our municipalities will only be using the water pipes for fire fighting and most of us will be drinking water like space station astronauts do:
http://www.scientificamerican.com/article.cfm?id=new-menu-item-on-space-st