It turns out it's a sketch, part of the Flemish series of mockumentaries "In De Gloria".
In 2006 one of the sketches, "Boemerang" (Boomerang) gained notoriety on YouTube. It features the host of a talk show, "Boemerang", breaking into fits of giggles after hearing the voice of one of his guests, who spoke in a squeaky manner due to a failed tonsillectomy. The video uploader who added English subtitles to the footage implied the footage was real and shortened it especially to remove all indications of it being fake. The full sketch shows the TV host in a supposed archive TV show (hence the title Boomerang) looking back on the infamous moment that got him fired in the past. All people in the footage are actors. The show's host, Erik Hartman, is played by Tom Van Dyck, his two guests Valère and Marijke are portrayed by Lucas Van den Eynde and An Miller.
This is confirmed by imdb:
One of the sketches ("Boemerang") about a presenter not being able to hold of his laughter during a serious talk with people who are the victims of medical blunders is often mistaken for real (by non-Belgian audiences). It was featured on 'The Tonight Show with Jay Leno' and gained some Internet notoriety through it's popularity on YouTube.