Bah. Humbug. For reference, the picture on which they base this design:
Is clearly simply a $\frac\lambda2$ dipole, meant for coaxes fed with a symmetric/ balanced signal, or producing one. The more alike the width of the tube and the upper copper antenna part are, the more "ideal" the dipole becomes.
In the way they use it here, the copper pipe is part of the ground part of an unbalanced receiver. So, this simply is not going to be great. What you want, as discussed in the comments, is a ground plane for a $\frac\lambda4$ monopole. And 45° radials is a well-proven, well-tested, pretty-close-to-perfect, foolproof way of implementing a seemingly endless ground plane.
For the length of the can in your picture to have effect, there would be the need for a current to flow in the lower parts of that. But that current can only flow if the can is not doing its job of simulating a perfect "E-field mirror" overly well (otherwise the energy "reflected" back into the upper half-space would be 100% of what incides at any point of the plane, and since the monopole is the only driven element here, it would surprise me if the currents induced at the part where the bends start actually help very much with making this a better antenna.
So, yes, they'll be getting better reception with that at 1090 MHz than with the stock TV antenna, but that's not hard. Simply replacing the $\ne\frac\lambda4$ monopole of that (e.g. by cutting it to the right length...) and placing the antenna on a conductive (magnetic, if possible, that's why it has a magnet in its pedestal) will probably do even better.
I rant about this far too often, but this is the year 2016. Antenna theory has been around for >100 years. And yes, physicists and EEs in their labs played and play around with all the conductive stuff they can get easily to build their antennas. So if someone shows up with an antenna design that seems new, expect them to use some sort of simulation, or an anechoic chamber with a reference antenna to measure against, before believing any advantage.
Really, EM simulation is not that hard these days, and with OpenEMS, it's available for free (I'm sure there's more ham-friendly software than that, though!), and I've met more than one person who claims to have designed the perfect antenna based on the Standing Wave Voltage Ratio at the desired frequency alone. Do you know what has perfect SWVR over a huge range of frequencies? A proper matched-impedance terminator.
For example, I have a friend who went to a rather well-known faculty at an US uni for a research internship, worked on and measured their newest antenna design idea, just to figure out the antenna was so inefficient, it was converting far more energy to heat than it was emitting radio waves. The prof wasn't disappointed at all – in the end, there's also needs for good absorbers and terminators, especially in isolation applications, so this was well worth keeping in the knowledge for future investigation or publication.
The point is you can't know if your antenna is good or bad without measuring its emission or at least simulating it. So, if not backed by solid data including a directivity and frequency chart, I simply apply "skepticism" as default reaction to antenna designs. And so should you.
