I think the marketing guys got a little bit carried away with those claims. 10dB increase in output is significant but it's not 10 times higher SPL. Subjectively speaking, 10dB higher SPL is roughly perceived as twice as loud.
Normal subwoofer implementations essentially place the listener inside the larger box of a band-pass design. In this design, low-frequency roll-off can be significant depending on the size of the box that the subwoofer is placed in. The larger the box, the more significant the roll-off. This is why small box subwoofers became all the rage. In addition to taking up less space, they provided deeper extension into the lower bass region. Small box woofers are, however, incredibly inefficient due to their heavy cone mass that must be used to balance the stiff suspension that is needed to match the small volume of the box. The way to combat this is to increase the magnet size, which is why modern car subwoofers have such humongous magnets.
The reason the fresh air sub works differently is that it vents to the outside of the car. So instead of sitting inside a bandpass box, the user is sitting inside a semi-sealed box. The deep-bass roll-off for a semi-sealed box is much shallower than that for a bandpass box, so the listener naturally gets more bass output. Additionally, since the interior volume of a car is huge, the subwoofer can use a fairly compliant suspension and thus very light cone mass to get the desired resonant frequency tuning. This makes for a potentially very efficient driver if combined with a reasonably-sized magnet.
It's just that most people don't go cutting holes in their car's chassis when installing subwoofers so this is rarely done for DIY or even most professional car audio systems.