NPR is not a public broadcaster in the sense of other nation's public broadcasters.
It was founded, initially, with funding from congress, as an independent, non-profit broadcaster. Currently, NPR receives very little to no funding from the Government. Something like 2% of NPR's funding comes from state, local, and national government. Though individual stations may receive radically varying amounts of government funding.
It is Public in the sense that it serves the public interest and is funded by listeners.
They're not government owned. They're get a subsidy through the appropriate government agency (don't remember the name at the moment) but it's only about 10% of their budget and they are free to act however they wish.
NPR is not state media. That would be Voice of America, which is not allowed to broadcast in the US.
"According to the 2009 financial statement, about 50% of NPR revenues come from the fees it charges member stations for programming and distribution charges."[0]
They are not government owned. They take grants but they are prohibited from taking money directly. A large part of their income comes from member stations who pay for access to shows, content, and support.
"Legally speaking, NPR is a private, not-for-profit corporation chartered by the District of Columbia and qualified by the Internal Revenue Service as a "501(c)(3)" organization exempt from taxation. "
I don't actually think the government owns it. The government provides some of it's funding (not all, though, which is why there's always a fund-raising drive?).