Huh?! Are you serious?! lot's look all the elements of the story independently and with respects to their proper timeline.
2001 Rick Perrys policiy for Bi-national Healthcare SPECIFIES setting aside an additional $4 billion to the Medicaid program, and more than $900 million to the Children’s Health Insurance Program. At the same time he urges legislators (NOT PRIVATE HEALTH COMPANIES) to pass a telemedicine pilot program that will enable, through technology, a sick border resident of limited financial means to receive care from a specialist hundreds of miles away
The article you point to is seriously distorted in it's timeline since it talks about a study done in 2003 and released in 2005, that proposes selling private health insurance to illegal immigrants to reward them and protect them for entering the country illegally. (Which apparently wasn't commissioned by the state of Texas).
Anyways the original WaPo article doesn't actually source anything to the 2001 claim that what Rick Perry was proposing was based on private health insurance.
Again.