The comments already cover that they broadcasters may well not have wanted to advertise another channel, however...
Before the "everybody in the world has 147 channels" era.
TV stations didn't use to ident all the damned time. They assumed you already knew what channel you were watching. If the channel had adverts, then they would ident in and out of the ads, or between shows, but at no other time.
I understand this may not apply to the US, which was already famous back in the 80s/90s for "57 Channels and Nothing On" but the rest of the world was well behind on this broadcasting plethora.
Another real world reason they had the recording without ident in the first place is that the ident is added at broadcast, so won't be on the recording itself. That way any channel can licence the recording without needing to obscure an existing ident.