The first video he does say 'arm straight away from the body' in the beginning only to emphasize to absolute first timers to keep your arms away from your body while in the ready position and to not have your elbow scraping your ribs when you swing. I've seen all of his videos before. If you watch part 2 where he actually gets around to hitting a forehand you'll see he uses and demonstrates a double bend. He also uses only double bend in his other videos such as this one he has on the crossover step:
The instructors in the 2nd video both use bent arm forehands. The one guy was demonstrating one facet of the brushing motion and exaggerating with a weird motion for illustration purposes as the other guy was addressing some point and he made his arm straight for some reason as he was being hand fed balls. It's kind of weird. When they start hitting live balls they are using dbl bend. I've seen all of the videos those 2 have as I am subscribed to both their mailing list and video channel. They both have bent arm forehands and always describe the double bend in all of their videos.
2 examples from them:
The 3rd video is a video discussing the technique of Federer and Verdasco! Both straight arm users. It's not a how-to video explaining how to hit a forehand.