I videotaped my first public talk as do many in our tech savy world. Videotaping is permissible at assembly and conventions as long as the equipment us not causing a hazzard to anyone else and it is used separately from the official sound/electrical system used by the convention committee.
As to locally videotaping, this would be allowed or not allowed as per the local Body of Elders. If your friend was intending to videotape himself, a first talk of a family member or bible study, the elders could have allowed it. But it is their decision. With the congregational and elder problems coming out on the internet, the elders might be feeling pressure to contain ways that their words might be used against them and so they ban local taping.
They would'nt use that excuse but they could use the issue of privacy of the other members of the congregation. The School (and Service meeting following) are not listed as public meetings so the privacy issue could possibly be used. But the Sunday talk and Watchtower Study, those ARE open to the public so priviledge of privacy cannot be claimed by the elders or anybody present.