Well, it seems that Granada TV had filmed the Beatles at the Cavern on August 22 1962 but were unhappy with the recording aspect of the film. So it was on September 05 1962 that Granada TV brought their tape recorders and recorded the Beatles re-performing "Some Other Guy" and the idea was to sync the audio to the film. Simple enough (assuming that The Beatles played the song at the same tempo as the previous performance, I guess).
Anyway, two songs were recorded: "Some Other Guy" and "Kansas City/ Hey Hey Hey Hey". The introduction to "Some Other Guy" is once again supplied by Bob Woller (Cavern in-house DJ) with the words: "OK, this is it. The Beatles sing 'Some Other Guy'". The introduction to the "Kansas City/Hey Hey Hey Hey" is done by Paul with the words: "Had a couple of requests to do a tune called 'Kansas City' , so we'd like to do 'Kansas City' ".
This alternate version of "Some Other Guy" can be found on the vinyl bootleg: "The Stereo Walk" as well as the CD "Puttin' On The Style". The version of "Kansas City" can be found (in a shortened form) on the "Anthology" documentary DVD/ VHS.