Could the resistor just as well be placed between ground and the switch, with the reset pin connected directly to the power rail?
Figure 1. The pull-down resistor idea.
I suspect that if you had drawn the circuit out as shown in Figure 1 that you would see the error of your thinking. (Note that it makes no difference whether R3 is above or below SW1 as it is a simple series circuit.)
When SW1 is press EN is still at V+ and R3 is now connected between V+ and ground so, for a 5 V supply 0.5 mA will flow through it. EN will not be affected.
The idea with a pull-up is that it is strong enough to hold EN high in normal conditions but weak enough that when a direct short to ground is applied only a limited current will flow. You can think of R3 in your original diagram as acting a little like a rubber band pulling EN high and when EN is pulled low the band stretches without harm and pulls EN high again when it is released.