How do movie makers navigate point-of-view among still characters
You assume that the Matrix technique cannot be used to weave a camera among people. The exact same technique - a combination of multiple cameras, cgi, and interpolation - can do exactly this. 

That said, the Flash has much more mature cgi technology than the Matrix, and in fact is famous for the cgi quality. Check out this video for some behind the scenes info. The majority of the intro you mention appears to be cgi.