Scott,
I believe it was an adaptation. As I mentioned, the 12th at St. Andrews immediately comes to mind with the false front, and I am fairly certain a lot of other greens there "fall" into the fairway.
Something to think about: Would you consider the Valley of Sin to be a false front or a different type of feature in its own right?
I also believe that since there was more of a reliance on the ground game during the turn of the century and not a very coherent definition of "green," "fairway," et al. that the feature of a fall off at the front of the green transfered and as mowing patterns, etc. became more in vogue the various courses and architects kept the fall offs at green length mowing-wise.
Tom Paul's suggestion seems to be more in practice nowadays at least. The par 3 seventh hole at PSU's White Course (Park, 1922) has a very severe false front, and the green is roughly thirty feet higher than the tee. The only part of the surface visible is the false front fromt he tee and it pretty much falls in line with the width.