Whatever the flow, the routing seems to have been changed extensively. And perhaps not just the routing. My understanding is that Muirfield was considered to be a pretty poor course initially, and only became great through years of improvements. Here is Harry Hilton writing about the course in 1906:
. . . Whether Musselburgh at the time [1892] was a better test of the game than the initial course at Muirfield is a question best left to those who were thoroughly acquainted with both links, but if Musselburgh did not provide a better test than the course over which the Championship was played in 1892, all I can say is that the Championship never should have been played over Musselburgh, as when one looks back and reflects, it is more and more driven home to one what a shockingly indifferent course it was. It lacked length, it moreover lacked condition, and altogether there were about four good holes on it. In later years someone set to work and attempted a metamorphosis at Muirfield, and the man who did it accomplished wonders. He got more out of the ground than ever appeared possible, and as a feat of golf links architecture it stands unrivalled, as, in the first instance, he obtained length, and that was very difficult in such a confined space, and moreover he managed to eliminate several indifferent holes. That was not so difficult on account of the fact that he had so much material to work upon. And, again, he considerably improved many of the holes. In fact he accomplished just about all that was possible for a human being to do; and still there is a doubt whether Muirfield is quite a sufficiently good course to merit the distinction of a Championship being played over it. The truth is, nature has not been sufficiently kind to allow a first-class course to be built in the space at command, and, again, the hand of man has built a wall round the links, and that wall is neither fair as a hazard nor is it picturesque in appearance. . . .
I am not sure to whom he was referring, but I don't think it was OTM.