To lamphs: of course a driver can adjust the route, but only to maximize his income. With UBER upfront pricing, you are not affected, only for waiting time. Keep in mind that drivers get paid for time and distance, so UBER will offer the driver the fastest and shortest route combination from a-b, but a driver may take a different route to maximize his earnings. It is called long-hauling. Drivers can get deactivated by doing this too much, or abusing it. Taking too much time, rider complaints and there is a fare review, however, they can also use a longer route, but get the rider on time to its destination.
As for the different routings, happens all the time.