An apparently ambiguous two-way stop

The TTUHSC parking connects to the Texas Tech parkway at a two-way stop, even though it is a T-shaped intersection. The parking lot street forms the base of the T and the parkway forms the arms. One direction of traffic on the parkway does not have a stoplight (the right arm), so people turning left from the parkway into the parking lot always have the right of way. Since this is can be a rather precarious intersection, there are several brightly colored signs facing the opposite direction of traffic on the parkway (the people who have to wait for the left-turn-ers) that have flags around them and they say

ONCOMING TRAFFIC DOES NOT STOP

I never knew there were so many different ways to interpret this. Just today I was coming back from lunch, and I was going the direction that doesn't have to stop. There are two lanes of traffic that go the opposite direction on the parkway (the direction that does have to stop), and the car in the left lane had stopped and was waiting for me to turn left, but the guy in the right lane started inching into the intersection before I got there. By the time I got to the intersection and was ready to turn left, he had almost completely blocked me from turning left. The best part is, he saw me coming, and I expected him to just finish pulling through, but instead he just stopped. I had to veer left and then snake around the intersection just to avoid hitting him.

I used to think Kansas drivers were the worst, and then I moved to Oklahoma and I thought Oklahoma drivers were the worst, but man oh man, I think Texas drivers take the cake.