May be it is just a coincidence, but our family cat who doesn't like close cuddling, sitting on humans or human lap at all, comes to my lap, sits and sleeps with me, licks, bumps by face and meows to my face whenever I am sad, feeling bad...etc. It's very easy to observe this, because she doesn't do it any of it in any other circumstances. I mean she sits beside me on a chair, but that's it.
I'm not the one to load special meanings or conciousness on animal behaviour, but the change is drastic. I think our pets are conditioned to our ordinary, normal behaviour. In a way they 'know' us and when we present even a slight difference, they kind of get that something is different. I don't mean 'knowing' or 'understanding' or even showing 'care', just reacting to a different situation that happens time to time. But it is in the end, 'attention' when you look at from human point of view.
You are probably going through something and I guess, feeling bad? (Your great grandma.) So from a romantic view, they are showing that they 'care' about their human.
PS I thought thought had an all white one, too? You had 3, didn't you? Or may be I remember it wrong.