The allegations were made against the network after the BBC did a highly critical documentary on the religion, The Telegraph reported Sunday.
While filming the documentary, veteran BBC reporter John Sweeney lost his temper and screamed for 30 seconds at a member of the church.
The video of Sweeney's outburst was put on Youtube by the church and Scientologists also created their own documentary of the BBC crew filming them.
Sweeney has apologized for his outburst, admitting it was "wrong and stupid," the British newspaper said
The BBC's documentary will be aired Monday on BBC1.
The editor of the documentary, Sandy Smith, spoke out about the allegations that the BBC had orchestrated a demonstration against the Scientologists while filming.
"Their DVD contains two grossly defamatory claims about us -- one, that we staged a demonstration against Scientology and two, that a terrorist death threat was made," he said. "It is absolutely outrageous to suggest that the BBC would organize a demonstration -- why would we?"