I saw a very moving presentation at a nursing conference a couple of weeks ago from Barbara Pointon (she was in the Malcolm and Barbara programme on the TV a while back, about her husband who had Alzheimer's) - she explained that one of the misunderstood elements of Alzheimer's is that the patient really believes that they are in past years, and it helps to humour them. Your nan probably didn't recognise her son in the older man who visited her, in her mind her son was probably still a teenager or younger. Barbara told us that if they want to go "home" from the care home, they mean their infant childhood home, they have regressed and don't recognise the here and now at all. (I hope Ratter can confirm what I am saying, I am a layman but work with nurses as part of my job.)
Barbara is now spreading as much information as possible to all healthcare workers about this cruel condition - if you can, take a look at the programme, there's a link to it on here at the bottom
http://en.wikipedia.org/wiki/Malcolm_Pointon
As you say, so hard for the carers - but as Barbara says, if you can at all get your head inside the patient's head, you can start in a small way to understand how they think they are viewing the world.