The actual sequence of hand-hand shutter speeds should actually be marked: 1/30, 1/60, 1/120, 1/240, 1/480, 1/960.
Light meters measure exposure values. When they say 1/1000 at f/4 they mean 1/960 at f/4. They do not "compensate" for the "non-linear" progression (actually, non-linear on a logarithmic scale) of what is printed on the shutter selector.
Producers mark 1/1000 but when one measures the exact performance of a shutter one would ideally want a perfect shutter to give 1/960 of exposure. If it does it's not a 4% mistake, it's fine. By the same token, if the shutter exposes for 1/860 it's not a 14% overexposure, it's a 10% overexposure.
Testing shutter precision by making several exposures at different shutter speeds with uniform light, compensating with a varying lens aperture, gives indications only about that particular diaphragm/shutter speed combination, not about shutter precision, as lenses tend to introduce an error also, the actual f/value is not be what it appears on the barrel (to say it more properly, the f/value does not coincide with the t/value).
Aperture "mistakes" are particularly strong at the extreme of the aperture range. Also, vignetting will be more pronounced while a lens is used at full aperture so one should consider only the centre of the image.
If one wants to know the exact speed of a focal-plane shutter there are electric devices which are relatively cheap (search on APUG for shutter tester, shutter accuracy etc.).
The problem with those is that they give proper measurements only with focal plane shutters, not with leaf shutters. Use of those testers with leaf shutters is probably at the base of the common (mis)belief about 1/500 in central leaf shutters to be something like 1/250 or 1/300 in reality.
I also, like Ralph, like to know exactly how a certain piece of machinery performs. I have had all my SLRs tested by a guy who gave me the exact time for each shutter position of each camera. I would have already bought a shutter tester if I had found a model which would work also with leaf shutters.