Yes, I agree. I don’t think Gillian and David “play” their behavior in any occasion. That’s just the way they are.
David is by nature quite handsy with people. When you watch his interviews, he’s always touching even petting interviewers, he never hesitates to hug or shake hands when you meet him. So it’s not really surprising he acts like that with Gillian who he knows for two decades.
On the other hand, we know Gillian isn’t comfortable with touching or even being physically too close to others. But she’s very different around David. She always searches for his contact, she touches him all the time and it seems like they have their own body language in their own bubble, and it looks totally natural. Always.
The best example that is coming to my mind is her last interview on Jonathan Ross. She was sitting next to a dude who grabbed her neck at some point. You could feel her discomfort and annoyance the second he reached for her. She froze and her whole body tensed. Compare that to when David grabs her neck during the Cutting Room. You have everything there.