The answer is in your question.
You are seeing a -0.125" vertical displacement because you are specifying a 0.125" gap in your vertical restraint. Do not think of the gap as "horizontal gap", for that you would use a Guide with a specified gap. So the pipe is "falling" because you specified a gap between the bottom of pipe and the support.
In other words, when you specify a gap you are specifying a certain dimensional space between your pipe and the support in THAT specific direction (your case being in the Y-axis).