For the specific question regarding the Fed video, he clearly has a cont. grip when he hits the bh overhead. Though he doesn't use his left hand to help as he usually would, I'm pretty sure he changes grips as he's running for the forehand. By the way he takes the racquet back and the WW type swing path I'd say he's in his normal Eastern-ish grip.
To the more general question of shots well inside the service line I think it kind of depends on several factors. First I'll say that I think this specific situation is where changing grips from your normal fh grip to a continental is a totally valid option. Potentially you're hitting a ball that's going to be more like a volley than a GS, so switching to a cont. is a reasonable way to go.
One important factor is the ball that you're hitting. Is it sitting up, low, fast (unlikely given the placement), are you running for it or do you have time to set-up? Another big factor is what are you trying to do with it? Drop shot, hit it hard, hit it hard enough to be out of reach, lob it (it is an option in some cases), just place it out of reach. The last big factor is what do you feel comfortable with and what shots do you own? If you hit with a full W. it's going to be hard to hit anything like your normal fh, but that grip makes it relatively easy to swiing sideways across the back of the ball (L to R for a rightie) and hook it back over with a nasty bit of side spin.
Back to the Fed video, I think he went with his normal fh grip because the ball was hit out wide to his fh and he wanted to get some topspin on it with a bit of pace. Nadal was up at the net, so Fed knew that going dtl with just a bit of pace would be enough to get it past Nadal for a winner. It would have been more difficult to hit it as hard as he did and with as much topspin with a cont. grip and keep it in.
Now if Nadal had been on the baseline and Fed would have hit that same shot, Fed would have just been feeding Nadal an easy sitter. In this scenario I think Fed might have stayed in cont. and angled the ball cc, as parallel to the net as possible. A drop shot with back spin would have been another response, also in cont.
Assuming you're still reading this, that cont. grip is generally a good choice for the low and close stuff because you're probably not going to be trying to come over the ball, but rather get underneath it, create some angles and/or backspin, and probably be ready for a volley.