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Yeah it was an entertaining video. That girl even introduced them as THE Muse so you have a point, she probably wasnt exactly clued up on the band.
Top of the Pops (a UK top 40 type show that aired on the BBC for a long, long time) often made bands mime (someone may be able to confirm exactly for me because they DID sometimes have live bands and sometimes not) and I remember watching Oasis on TOTP when I was about 11 and they swapped places. They also said it was because they werent given a choice and werent permitted to perform live.
Nirvana did this on TOTP:
Also, this wasn't the first time Muse has done it: