Fair point as this person does want something. They want that friendship back.
If an old friend adds me on Facebook and then starts trying to sell me some vitamin programme that is very different to if they add me back and are like "Oh man I've missed you, I deleted Facebook but it's so hard as an adult with a job, etc. to keep in touch with people isn't it? How you and the family doing? I'm sorry I just cut off contact like that, I thought it would be better but I was so wrong".
It all depends on the motives and actions. It seems this person is sincere in that they feel they really screwed up just cutting all social ties how they did.