@thistlejak has it right here - as with my parents, it became about their individual needs/wants as opposed to them being a couple. We stopped worrying about what people might think (why aren't they together?) and looked at what they needed. My father now has Alzheimers, but at the moment is still indpenedent in his own home. He never mentions my mum, who died a couple of years ago. I honestly think they were happier apart - though this may not be the case for others.
I learned to "shut down" people asking why my father stopped visiting, I think the staff may well have seen, from his earlier visits, that they did not get on. After a while, it was no one else's business.
As to whether they both understood the implications of living separately - my father certainly did, at that time, and got on with his life. My mother wasn't initially that keen to go into a home, but liked "day care" sessions there that we arranged for her and when she moved permanently, got to know, and enjoyed winding up the staff. They were great with her and I really feel this was the best option.