I think I figured out the source of the confusion about filming an episode of Chopped. According to the link below, they tape about 80 hours of footage for each show, but that doesn't mean it takes two weeks.
The chefs are there for a 12- to 14-hour day. During that time, they might film Ted Allen saying his opening lines several times. They have nine cameras recording the chefs and judges from different angles for 20 to 30 minutes of cooking time for each segment. After each contestant is chopped, producers interview them for the comments that are eventually shown while they're cooking. Then there are the location recordings of each chef's introduction at their restaurant, home, wherever they work.
So all that would add up to 80 hours or more of footage per episode, but it would only take a couple of days to accumulate that. I imagine the judges are playing on their phones while the crew cleans up the set between segments
Shooting Baskets: Behind the Scenes of Chopped : Shows : Food Network