Yeah, just because a channel is public broadcast doesn't mean some of the content it shows hasn't been commercially produced, and a license purchased for that country's geographical area only.

I've tried watching some Italian TV channels, and some content was not available for streaming. It's a common practice here. It also applies to satellite-transmitted channels, they usually don't have the license to show some movies on that version (you can only see them on the terrestrial signal).

NFL season will likely stamp out the CBS and FOX streams in the US.