I just did a little more investigating. I went out and felt the metal drain thingy that the water is coming out of...it is hot to the touch because the water coming out is hot. I went into my garage and climbed up to feel the (copper?) coiled pipe-thing that takes the hot water out of my tank and into my house for use. It is hot to the touch (which I would expect). Then I felt the coiled pipe-thing that leads from the tank into the wall (and therefore out to the drain), and it is NOT hot. It is the same type of pipe as the one that carries the hot water into my house...so wouldn't it be hot if it were draining hot water outside...especially since the spigot it is coming out of outside is also hot?
So I'm pretty sure its the neighbor's tank. Does my deduction sound accurate?