I'm afraid it's the other way around, and tires eventually slide as a result of understeer. One of the biggest misconceptions about under and oversteer is that there isn't any under or oversteer until the tires start to slide. The slide is only the symptom, but understeer and oversteer occur long before the limit of adhesion is reached.
So what you're saying about the BMW understeering at 10 mph is absolutely correct. In steady-state conditions, it understeers at 5 mph, 10 mph, 150 mph, and everywhere in between. I can still be induced to oversteer at any of those speeds depending on brake and throttle input, but in steady-state conditions, the car understeers.