We are an air refueling unit, but they have these little dart-shaped planes like the T-38 as well. Not sure why we have them (maybe so we have planes to fly to help train the fueling unit?), but I know they're part of the local operation. They talked about them on a tour I took of the base a while back, but I can't remember for certain what the plane was called. Plus I see them flying around nearly every day. Some of those pilots like to open up the throttle on the way up and it makes a nice sound. And by nice I mean really, really loud.
To my knowledge (being ANG - no not in nebraska), Nebraska doesn't have T-38s only the KC-135. The T-38 are used to train fighter pilots to assist with getting used to pulling high g's (major reason that NASA uses them as well). Granted, i haven't been there in a long while but the unit in Lincoln has no purpose for T-38s. They had to have come from out of state. The story about them coming from Texas makes since because our largest T-38 training unit is based in San Antonio with a few squadrons scattered around.