Based on the summary on NPR’s website–I can’t listed to audio at the moment–this doesn’t seem to have anything to do with vouchers. Vouchers allow poor students to escape from failing public schools by attending private schools instead. Each private school has its standards for admissions, and any poor student who meets the standards can attend. This case has to do with a different sort of program, which allows students at failing public schools to move to other public schools.
It’s worth noting that vouchers are not a conservative cause or issue. Liberals happily and proudly promote the same basic idea in many areas. For example, way back when, this country attempted to provide housing for all poor people by herding them into gigantic housing projects constructed and run by the government. That was a total failure, of course, so now the government instead gives poor people housing vouchers and lets the free market take charge of decide where and how to build the housing for the poor. Likewise, the health care “exchanges” under Obamacare will use the same general principle. The free market decides what to offer and what to charge, subject to certain regulations, and the government provides subsidies to the poor so that they can afford to buy something of their own choice.
The real mystery is why liberal Democrats are almost uniformly opposed to education vouchers while at the same time being happy about vouchers in other areas.