Jellyfish are not active swimmers--they ride whatever current is in the water. In square tanks, this causes many species to get stuck in the corners where the water is stagnant.

Also, this means that they can't fight the current and generally get sucked into the filter intake. At the same time, they need strong current (see the comment about them getting stuck in stagnant areas) so you need a filter with a strong intake.

Some species, like moon jellies, all you need to do is diffuse the intake. You can see a section in the video where in the background they demonstrate a filter with the intake buried under a layer of marbles.

For other species, you need a specially-shaped tank called a 'kriesel'. (Do an image search for 'kriesel jellyfish' for some examples.) These tanks are shaped like a hockey puck standing on its edge, and move the water in a circle, so that no area is stagnant. Also, a water current blows across the filter intake, so the jellies get pushed aside instead of being sucked in.

Fun fact: The big jellyfish display tanks in Monterey Bay aquarium are actually oval-shaped kriesels with current blowing down both sides, and back up the center. That's why the jellies always seem to be upside-down--they're facing into the current in the center of the tank. :-)

I'd also disagree with the claim that jellies don't need any "exotic care": They're physically very fragile, and you have to be very careful to avoid damaging them when you clean the tank. They also require special food (notice that you're supposed to order special food from this guy) and high water quality, not to mention the special tanks already mentioned.