A couple months ago I started wondering about this very thing, so I went searching for any information that I could find about it. I did my best to ignore the theory-based opinions and "this happened to a friend of a friend" stories (of which there are many) and came to the conclusion that it shouldn't be a problem.
There are two seperate issues here: oil decomposition, and oil migration.
All of the cases that I found in which a watch had failed because of not being run were older watches that had sat around for years. It sems that the oils used back then were not completely stable and sometimes decompose into a gummy substance if left to their own devices.
This is the same thing that happens it you let a car sit in a garage for a few years until the oil starts to turn into sludge.
I was told by a watchmaker that the modern lubricants the industry uses now are much more stable than the older ones and gumming is not really an issue.
Conceivably the oil could migrate if the watch was left undisturbed in one position for a long time, but a watch does nnot have an oil sump like a car does. The oil is applied to each part individually and is to a large degree trapped inside the bearing, and therefore is much less affected by gravity than oil that must be continually pumped from a common supply. I was unable to find one example of a watch that failed because of the oil draining away from the bearings.
I would say that in theory these may be problems that could crop up if the watch experiences a certain set of unusual circumstances for a long time (much more than a week) but in realistic terms they are nothing to worry about.
