What you're talking about is the Lifeline program, which was established in 1985 and expanded to include cell phones under the Bush administration. The changes took effect later during the Obama administration, and so it got the nickname "Obama phone" by some. But he didn't have anything to do with it.
https://en.wikipedia.org/wiki/Lifeline_(FCC_program)
What you've linked is some unaffiliated site, the official website of the administrator of the program is here: https://www.lifelinesupport.org/
