The distinction is made, and can be found right in this passage:
"These schools have every right to teach whatever they want no matter how much I disagree with it as long as they are fully private," he says. "But when they take public money through vouchers, these schools need to be accountable to the public in the same way that public schools are and they must abide by the same rules." Kopplin is hoping for more transparency in these programs so the public can see what is being taught with taxpayers' money.
Saying that voucher schools need to be accountable to the public by following different parameters means exactly what it says, and doesn't even remotely imply getting rid of vouchers.
He didn't say vouchers were unconstitutional. His argument is that the use of taxpayer money in the form of vouchers to fund inaccurate religious curriculums was unconstitutional. Again, we've been through this before in that other thread. This is an entirely separate discussion from whether vouchers themselves are good or bad.
vouchers in 99 percent of cases can be used in religious schools, i dont even think there is a voucher program that can only be used in non religious schools, so for all intents and purposes attacking the fact that vouchers can be used in religious schools is an attack on the voucher programs