[orulz]

It's actually not 100% privately financed. It's private insofar as there is limited direct investment by the US, Texas, or any local governments. So, little of your tax dollars are going into it. However, I believe that the government of Japan is providing at least some level of backing for the loans, actually placing taxpayers of Japan on the hook - but they are betting that this investment will pay off.

The segment between Houston and Dallas will be basically financed along these lines, but it's not like there will be exactly zero public participation.
Public agencies will expend man-hours during review and planning for the line. Probably some right-of-way already owned by the state such as highway medians will be given cheaply or free of charge. The railroad, as a public utility, will also have the power of eminent domain conferred to it by the state (existing freight railroads, power companies, and pipelines already have similar powers.)

And, finally, the extension from Dallas through the Arlington/DFW area and on to Fort Worth will be planned and built by the public sector.