We can't "see" the Kuiper belt or the Oort cloud because they are simply distributions of very widely scattered objects. You can't hide behind them any more than you can hide behind the solar system itself, or behind a constellation of stars. (We can see individual Kuiper belt objects, a few of them so far anyway.)

Look at it this way. Can you hide behind a row of parking meters if you are walking past them? No. Well, these "belts" and "clouds" are many orders of magnitude less dense than a row of parking meters.

The whole thing is utter nonsense. Don't worry about it; have you noticed the Mayans fretting about the end o' the world in 2012? Yes, the Mayans are still around.