It's my understanding that this was pretty standard practice in the 60s/70s. This is a good example:
There was a legal obligation when playing on Top of the Pops that you could not use the studio recording from the official recording, you had to record a studio version just for TOTP (which makes these recordings collectible because they sometimes sound quite a bit different to and/or better than the previously recorded official tracks). I believe it had something to do with musicians' union rules for TV work which were back then very restrictive.
It wasn't just confined too TOTP: When Jethro Tull did Too Old To Rock'n'Roll, Too Young To Die for British TV in the late 70ies, the whole album was (had to be) rerecorded (within a couple of days or so).
Tull actually liked that later, livelier studio version (they are not playing live in the TV show as you can tell, inter alia, by the simultaneous singing and flute playing of Ian Anderson) better and it is what you hear today when you hear the 40th Anniversary remix of TOTRNR, TYTD. The masters of the original TOTRNR, TYTD only exist in part any more, they were accidentally wiped some years ago.