The strengths of the Tricaster is multi-camera and live-to-tape productions. One small box to do the show. The Tricaster is aimed at multi-cameras production that are done live, streamed, or taped.....I believe it will some editing, but I think they mean the Video Toaster. Software that goes in a PC. Switcher, Editor, Paint Box, CG, DVR's, and Lightwave...
If all they want to do is edit....Your suggestion is fine...If they want to do a live-to-tape show, Video Toaster