One of Thorn's great admonitions against short stems is that they might put the rider's hands behind the "centre of steering" thus causing an uncontrollable wobble or shimmy.
Only if the bike is inclined to shimmy in the first place. Colin's points are right re shimmy, I'd say. It's a resonance related to the spring or stiffness of the frame and the front end trail, and speed. Tyres, pressure etc can influence it too as part of the trail 'system'. Resonance can occur and where your hands are may be part of resisting/preventing/controlling it but not a cause. Hand position can affect weight distribution and that's part of it, but again only if the bike can be prone to shimmy.
Hands behind the steerer tube -as I assume they mean by centre of steering?- isn't an issue in itself. I have both a very short-stemmed drop-bar bike and a bike with swept bars where my hands can be a little behing the steerer tube or well in front, ie all poitions around the steering axis. It doesn't cause or influence shimmy, loaded or not. One bike won't do it as it's plenty stiff enough, the other I can induce a little wobble at a certain speed with luggage on the bike by artificially flexing/steering the bike, but it won't resonate naturally.
For ANY BIKE that is light enough to be comfortable to ride unloaded, there will be a set of conditions (load, rider weight, tyre, wind, surface) which will cause a shimmy.
You might not have found it yet, but its there all right.
Totally agree. I know of plenty of bikes that have been criticised (or at least critiqued) for being stiff, but they are far less prone to handling wobbles or even a shimmy when loaded than some slimmer-tubed bikes. For off-road or rough-road handling, imo a short stem adds control and increases your ability to correct a momentary loss of grip, or react to undulations in the surface mid-corner (assuming your bike and load suits this sort of riding in the first place). For riding steadily on good roads it's not an issue though, more traditional road geometry and fit, stem dimensions etc work fine.