Cocktail history is a fickle thing, so it's tough to ever speculate on there being a definitive truth here. In Boston, the best cocktail bars will serve a neat Old Fashioned -- it's a bit more elegant drink when stirred and strained, then garnished with orange peel or oil. The ice waters down the drink, which some may prefer (esp. if they want soda water too). If a customer wanted ice, I might try to talk them into a large cube rather than many small. Eastern Standard referred to it as a 19th Century (http://www.fourpoundsflour.com/wp-con...)
The wikipedia entry lays it out accurately, suggesting ice and fruit are modifications:
However, to avoid strange looks, you can just order a "muddled old fashioned" which should always come on the rocks. Otherwise, muddled fruit floating in liquid ain't pretty!