I'm always a little bit suspicious of people who claim this, actually.
It's easy to say that people have 'emotionally' left the marriage a long time previously and that means they are ready. Having been in the situation myself, I'd say that, yes, you can emotionally separate from the marriage even years beforehand and, therefore, not 'miss' the other person, or experience any heartbreak. It's also possible to experience a huge sense of elation, freedom and relief.
In my experience, the 12 months after my marriage ended were the happiest of my life - I felt lighter; more free; more confident; hopeful... I spent a year walking on air and that I was unstoppable.
However, I think that people need time after a relationhip ends to 'recalibrate'; rediscover themselves; work out if what they want out of life/a relationship is the same as they wanted when that relationship began...
I know that, although my marriage was shocking, I learnt a lot about myself within it. I changed, I grew, I matured and it took time afterwards to really understand who 38 year old me was. And it wasn't the same person that 25 year old me had been. I met a few men in the first few years after my marriage ending and, whilst they were mostly reasonable men, it's taken 7 years for me to feel like I would want/be able to commit to another person properly.
I also wouldn't want to be with someone who had just left a long term relationship for those reasons. I'd be wary of someone who felt they were able to 'move on' quickly. I think it's healthy for people to spend some time alone in order to 'connect with' themselves again. Nothing at all to do with getting over someone else.