The USDA FSIS puts out Time-Temperature Tables for Cooking Ready-To-Eat Poultry Products (PDF). They recommend holding the fattest parts of a chicken at 140°F/60°C for 35 minutes to ensure safety.
The time is increased greatly as you lower the temperature only a little (for example, it becomes 53 minutes 138°F, a mere 2°F lower). If you raise the temperature a little, it's much shorter (23.5 minutes at 142°F). As he says in the video, the food safety agencies recommend a higher temperature—the normal recommendation is 165°F.
The 165°F is to allow a safety margin, in case:
- Your thermometer is off. As you can see, a few degrees make a lot of difference.
- The spot you probed wasn't actually the coolest part of the bird.
The recommended times in the tables are for the worst-contaminated bird the USDA believes you could run into, which is probably far worse than the bird you're actually preparing.
As to the juices, its doubtful they run clear at 140°F. But the color of the juices is not a reliable way to determine if chicken is safely cooked.
It's up to you (and the people you're feeding) how much safety margin you're willing to remove. But note that if you use an accurate & calibrated thermometer, probed in several spots to find the coolest, and take the bird to 151°F, then leave the thermometer in as it rests, as long as it stays ≥150 for 4.2 minutes (≥149 for 5.4 minutes, or…), FSIS says its safe. That's still going to leave you pretty juicy chicken, though not quite as much as at 140°F.
Beware, it will not have the texture you expect!