It's very hard from a short anecdote like that to really see if applies in your personal situation. We have no idea why his W wanted the separation and what their problems were in the MR. It's also hard to say whether the 'friendship' is what brought her back to him. There could be a host of other factors that were in play as well.
I know what your fear is. I had the same thing - my W felt that I was not there for her as much as she wanted. But doing a 180 on that works if both of you are committed to working on the marriage. At this point, she's beyond that and so what you think would be the logical improvement you need to make isn't going to work. i know it's tricky. I would err on the side of giving her space, lots of it. Stay NC/dark; don't ignore her communications - keep a line open, whether it be text, email, phone etc that works best for you; decide how you will respond to her communications and what requires your attention for a response; always be polite and civil in your communications; and do the DB stuff like GAL, personal development in areas you need to get better at etc.
This one is hard and takes time, but you need to give up the want and expectation of her coming back. Drop the rope and go on your detachment journey and do what's best for you.
