In my experience, Murifield has not been impossible to get onto. I expect that Muirfield, and Prestwick, are the two toughest clubs in Scotland to play as an inunivited guest.* But by no means "impossible." Muirfield's reputation owes, I feel certain, to the hilarious old stories, most of them with a strong grain of truth, of the club's Secretary and starter, Paddy Hanmer. I shall always remember my own first encounter with Paddy Hanmer. Taking and passing the Bar Examination was easier, and less stressful, than my first visit to Muirfield.
"Impossible" = Augusta, Cypress Point and Seminole. Muirfield and Prestwick are easy by comparison.
God bless the Scots.
*Edit -- I can't speak for Loch Lomond, which I have not visited...