It wasn’t so much the sadness, it’s that both the Doctor and Clara are people who think they know better. That’s what they are. The Doctor always thinks he knows better; Clara always thinks she knows better. So what they do at the end is a perfect summation of their relationship. They lie and endure pain and loneliness in order to protect the other because they think they know better. Amy would never have done that; she’d have told him what happened. But, people who are more controlling than that think they know what’s good for everybody else aren’t like that. So, Clara’s not the Doctor; she’s not the same person as the Doctor, but – the traditional thing is to say the hero and the archenemy are mirrors of each other. Are they? Are they though? Not really. I think it’s more likely that friends are mirrors of each other. If you watch any close friendship, the extent to which they start to duplicate each other is quite interesting, even with Dr. Watson and Sherlock Holmes. While they’re different people, they have similar appetites. So, yeah, it was the perfect way to say goodbye in that episode; each one doesn’t think the other can cope with the truth.