Think about the operation of a schmitt trigger. It's supposed to clean up a digital signal so it's always held at a 1 or a 0. For example, a digital signal might have a very slow rise/fall time, so it spends a significant amount of time in "no-man's" land as it changes state. A schmitt trigger cleans this up by slamming the output to one of the IO rails once the input crosses a certain voltage threshold.
One of the characteristics of an op amp is it has very low output impedance, which, in the case a schmitt trigger, you can think of the output as always being connected to one of the supply rails. This isn't the case in actuality, but the concept helps clear up some details that aren't really relevant.
So, since the output of the op amp is always connected to one of the supply rails (but never both at the same time!), R3 will always be in parallel with R1 or R2 (again, not exactly true due to non-ideal opamp characteristics, but close enough for this case).
EDIT Here's a little more detail about opamps:
Take a look at the internal circuitry of an op amp:
The output is between Tr5 and Tr6. Assume R8 and R7 are 0 ohm. We know from the operation of a schmitt trigger that the output will always be either V+ or V- (aka, the power supply rails). This means that Tr5 or Tr6 (but not both) will be on full bore. Ignoring the internal resistance of those BJTs (it's low enough not to matter), they will connect the output to either Vcc or ground.
An op amp amplifies the difference between the two inputs. The output is always the difference between the two inputs scaled by a gain factor. For example, if the + input is at 2.3v, and the - input is at 2.2v, and the gain factor is 10 (made up numbers for easy math), then the output will be at 1.0v. 2.3-2.2 = 0.1. 0.1 * 10 = 1.0.
Now, in real life op-amps, the gain is big. Really big. As in, so big that an itsy bitsy little difference in inputs will make the output drive to one side of the power to the op amp. The minimum voltage an op amp can output is the negative supply to the op amp. The max voltage an op amp can output is the positive supply to the op amp. So, if an op amp can 3.3v supply, is can only swing from 0.0v to 3.3v.