Andrew Gray wrote:
To the best of my knowledge, the United States does not possess any "royal parks". Given Stephen appears to live in the UK, a country which does have royal parks, it seems reasonable to assume he shot the videos there. In which case, the question of what American laws apply to the filming seems a bit less relevant.
While the person filming has to worry about the law regarding filming, anyone redistributing the films in the United States does not---it is not necessarily illegal to redistribute illegally filmed video. This came up a while ago on Commons with World Cup photographs: The stadiums prohibited photography, but given that photographs were taken and uploaded under the GFDL, Wikimedia is violating no law by continuing to host them. The original photographer likely violated the prohibition, but that's a separate matter, not enforceable through copyright, and so not really our problem.
-Mark