Definitely DO NOT GROUND (at least with the way you have it in your schematic). That changes the circuit by sticking a resistor in parallel with your desired variable resistor. When using a pot as a variable resistor one end pin is just left open.
Why you get the same result whether that end is connected or left open? I don't know. That doesn't make sense.
EDIT: I forgot, but you can turn a pot into a variable resistor by connecting up all three terminals such that the wiper shorts across the resistance to be ignored. So you could connect terminal 2 and 3 together (see (a) in Transistor's answer).
I guess you could connect to GND as shown by @Transistor's (b) example. That has a similar effect to what you described as wanting but sort of changes the "intent" of how you were thinking the pot would be used in your circuit so it didn't occur to me. You should probably pick his answer. It's better.