The last thing you'd surely want, if you were a soldier recovering in hospital, is any politician pestering you as part of some a public relations exercise. If Obama had done what he's being blamed for not doing, it would have been both not just politically stupid, but very bad manners.
There used to be talk about people carrying cars saying that, in the event of their being injured in am IRA bombing or whatever, they did not wish to have Margaret Thatcher come to visit their bedside.