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.
I can promise you we have similar planes here in Lincoln. I see them probably four days out of every week, minimum. They're not flying here from somewhere else, like the 747s and AWACs that come here from Omaha to use the runway for touch-and-goes. These planes I'm talking about are stationed here.
The fly-by planes for tomorrow are not the planes I'm talking about, which jives with the guy saying they're his cousin and wingman. These are different planes than what we fly, and definitely a different paint job. Ours are similar in shape, maybe a little smaller, and have a darker, solid paint job. Ours are similar in shape to the "MIGs" from Top Gun, if that helps.
I can back up that the planes based in Lincoln are indeed T-38s. I live just west of the runway and I see then all the time (almosy daily). They will often be training with f-15 "type" fighters (2 T-38s and 2 "f-15's"), and they shake the whole house some days. Two T-38's were flying today, as they often do the day before the game. I also noticed a c-130 that I normally don't see at the base.