The following might or might not apply to your particular situation with the Texas Tomorrow Fund:
In the event of a scholarship that is equal to or better than the Texas Guaranteed Tuition Plan, you can apply for a "scholarship refund." From there the money can go to the school, or you can direct it to a 529 plan. Both of these options will avoid taxation. If you take a cash distribution, taxes will come due. Texas Guaranteed Tuition Plan - Scholarships and Financial Aid
It is correct that you can have an out-of-state or private school send a bill to the Texas Tomorrow Fund, and then you would be required to submit the difference to the school.
The cash refund or scholarship refund rate is set year by year. It is set for this fall at $265.96 per hour. The following is from the website:
2012-2013 Academic Year average tuition and required fee rates
(Effective Fall 2012 - Summer 2013)
Cancellation forms received prior to September 1 each year will be refunded at the prior academic year rates.
•$85.65 for junior college plan hours
•$265.96 for senior college plan hours
•$693.51 for private college plan hours