In the last couple years I've gotten pretty proficient at that. I'm getting good at track stands too. Riding hands-free is really easy if you're going fast enough. I imagine those TdF riders are going a wee bit quicker than me.
I can't do it at slow speeds. A descent, tail wind, smooth surface, get me over 13 mph and it's no problem. I bet 13 mph is the slowest those TdF riders ever go!
Track stands are something I picked up because I stop at every single stop sign. I can't hang out in a track stand indefinitely and I don't actually recommend it the way I use it because it is confusing to drivers--they can't tell that you are stopped or stopping unless your foot is on the ground. And there are times that I put the foot down in order to send the right message instead of track standing. It's fun to stop at the stop sign in front of the police station and cease all forward momentum without putting my foot down. I doubt that the officers could tell that I came to a full and complete stop. (I've never gotten a ticket. and I highly respect & value our officers. It's just my own little rebellion.)
I didn't try hands free until I'd been biking daily for years. I didn't even like to try to drink from my water bottle. Now I'll text, drink (water), bike, rummage in my seat pack, eat a cheeseburger... (ok mostly joking. With the new touch screen smart phone I can't even text & walk much less text & bike.)
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike