No worries.
The D800 has roughly the same pixel pitch as the D7000 and as far as blur is concerned it will behave similarly. As with ANY camera, the less motion there is during the exposure, the sharper it will be. Nikon's point is that in order to extract the greatest possible detail that the sensor is able to produce, a greater degree of care is required. If you take a photo with a D800 and shrink the image down to 16mp or 12mp or whatever, the amount of blur would be the same as if the image was taken with a lower resolution camera. If you are making 8 x 10 prints you don't need to treat the D800 any different than your current DSLR. If on the other hand you are printing at 40 x 60 inches, then a beefy weighted tripod, mirror up and a remote release will allow you to obtain the best images possible. Think of it this way, the amount of blur is no greater, but the sensor is capable of resolving it to a greater degree. Practically speaking, the added ability to resolve blur that is caused by camera motion needs to be addressed if you want to get the best results from large prints. The other place it might become noticeable is when cropping.... A 6mp image from a D70 might very well show less camera motion induced blur than a 6mp crop from a D800. However, if the D800 image is taken such that the 36mp D800 image has the same viewfinder coverage as the D70 image, the 36mp D800 will absolutely blow the D70 image away. In this case you might find some blur in details that cannot be resolved with the D70, and the elimination of THAT blur may require better technique. In summary, the D800 will not take pictures that have more blur than what you may be accustomed to, but it will allow you to resolve more detail; and that detail may have a component of blur.

Unfortunately the Nikon answer simply re-creates the uncertainty by seeming to say that blur will be amplified by this camera because of its high detail. It suggests that blur would not be as noticeable as with a camera of lower definition. So more care will have to be given, especially if you want to enlarge the image significantly.

As a fine point, you cannot expect the sharpest images with almost any camera at low to moderate shutter speeds without the use of a tripod or other steadying device and even mirror lock up.

Thanks. However, I didn't interpret the guide in the way you did. The example they showed employs that shutter speed, and logically it might make sense, but I get the feeling (from the NIkon team's answer as well) it is an issue with the camera and your technique has to be flawless. The biggest issue for me is this, followed by lower ISO than I expected. The camera's features otherwise seem fantastic. I have been a lifelong Canon user, and I was ready to switch, but obviously have some concerns.