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They're definitely showing it. I saw the start of the coverage on NBC News Now at 10am UK time, and it's on right now.

It's showing on the live stream on their website but the satellite feed on Sky Q is showing Dateline for me and has been all day (not sure if it's the same show on a loop actually)

Ah, yes - it's the same on Now TV. I wonder if they're producing a separate feed just for Sky - and, if so, why, when there aren't any geographical restrictions on their other streams?

Staying with the US broadcasters, CBS's studio at Westminster Abbey seems to be in the same place as - or very close to - the BBC's studio for the Queen's funeral.