Inductance and capacitance have the effect of changing phase. It is literally their only job when it comes to antennas. This effect, however, has a wide range of uses, from shortening 1/4 wavelength antennas (possibly the most common use) to antenna matching. Changing the phase in this antenna is actually a combination of both of the above, although definitely less for matching than phase correction.
The model in the link you provided shows it is actually less than 180 degrees of phase change, which has me curious why they said it was a full 180 degrees. I would say it was closer to 1/4 wavelength of phase change, not the 1/2 wavelength they claim. The bottom element is also closer to 3/8 wavelength long electrically. When it comes to phasing, this length would match much better to the 5/8 wavelength element above. If this were a true 180 degree phase change you would have a 1/2 wavelength element on the top and a 1/4 wavelength element on the bottom, to get from the claimed 5/8 wavelength section to the claimed 1/4 wavelength section you would need 3/8 (or 135 degrees) of phasing, not 180...
I should also point out that inductors aren't the only way achieve the change in phase this antenna has, capacitors can do it as well, as well as phasing stubs, and all three of these methods will end up with a very similar feed point impedance, which calls into question the mentioned "second function" they mentioned.
The radiation pattern does look like a typical co-linear pattern, and it doesn't appear that the antenna is mounted that far above the earth either, although its length may be a bit deceptive here as it is close to 30 feet long if not a little longer so its probably at least that high above the earth in said model, although it does not include a mast, which depending on the situation can either help or hurt the radiation pattern.
I also like the fact that it can be direct fed without having to go through any matching circuits that antennas longer than 1/4 wavelength in length typically need. I think this is actually a bigger deal than most realize, and because of this it wouldn't surprise me if this antenna could handle far more than the 5kW of power the claim.
If you can get a structure that can handle that antenna at about 30 feet or so above the earth, I think it would do amazingly well, but its not going to be cheap...
The DB