Dave Lewison
EF1
Locking up the rear brakes will, in most cases, cause the back end to fish tail a bit, but counter-steering can keep you going straight, assuming you don't have a heavily crowned road (and you often do on muddy roads). Furthermore, downshifting does the same thing, but with even less control over the spinning/locking up of your rear tires than carefully applied and modulated emergency braking.
Well, I guess we should qualify if we're talking about a front wheel drive or rear wheel drive vehicle. If RWD, then I'd agree with you, downshifting has the same effect as e-brake. But in a FWD vehicle, downshifting provides braking to the FRONT wheels, which is where the majority of the vehicle's weight is, and also where the control inputs are felt at the road, so that's where you'd want braking applied if possible. Since there's less weight over the back wheels, especially as the vehicle slows down, they are more likely to lock up than the front wheels.
In either case, we're talking about maintaining control. You don't want to do either of these things (downshifting or e-brake) if you're going fast. And if you're blasting down a muddy road at top speed, you're probably gonna regret it!
But this is starting to stray off-topic.