I always wondered myself... So I did a short search on google and came up with the following:
'When Matt and Trey delivered the pilot to Comedy Central, they didn't have a bumper (you know, that card at the end of the show that tells you who created it).
Not having an appropriate company name or logo to use (Avenging Conscience notwithstanding), they tossed in the logo of Braniff Airlines - a defunct airline from the 60s and 70s - the music is the melody from "Cannibal." After the show aired, they were contacted by a company that owned the rights to the Braniff name and logo. An agreement was made to allow them the use of the logo on South Park broadcasts, but not on any other projects in the future.'
Hope that answers your question!