Again, to clarify: you're confusing the funeral with the memorial service. A&E, People Profiles and the in-house team who produced the Brian Henson TMS intros would have only received clips even of just the memorial. I doubt any of them got a full tape.
Speaking of the Peopel Profiles special, it's a nice piece covering Jim's days with thoughts and reflections from friends and family. There are also a number of articles related to the subject that you can dig up from circa 1990, starting with the Life and People Magazine articles I've transcribed and archived on my site linked in my signature.