The articles says the same thing, but they also tell why accepting these free programs is detrimental
"The problem does not stop with removing the dollar savings argument from our legislative arsenal. By accepting funds from the government, home schoolers provide a strong rationale for government control of home schoolers, a rationale which overwhelms any remaining savings argument and also blocks use of the religious freedom argument. Here is why. "
"Government is responsible to track and control what happens to its money. You and I want accountability for how our tax dollars are spent, and other citizens do too. So when tax dollars are funneled into home schooling, it creates an intensified state's interest in the home school educational process. The state suddenly has a new stake in your and my children's education. The state assumes responsibility for outcomes when its money is involved. That translates into state control."