Hmm...
Seems I've plugged some subs into the wall in my day:
http://www.betteraudio.com/geolemon/dscf0010.avi
(OK, I might have "modified" it slightly before I plugged it in

)
If that's what they are showing, they sure better show how they WIRED those subs, don't you think?
It's not the VOLTAGE that causes heat (and thermal failure) - it's CURRENT.
The W7 in particular - it's a 3 ohm sub. Or if it's the bigger one, they could have wired it to 1.5 ohms.
IF the L7 was the dual-2 ohm version, they could have wired it to 1 ohm.
Or they could have wired it to 4 ohms, and only 1/4 the amount of current would have flowed through it.
Simple Ohms law. V=IR, where V is voltage, I is current, and R is resistance.
Let's play out a scenario:
Let's assume they wired the JL sub to 1.5 ohms, and let's give them credit... Let's say they used a Kicker sub that was a dual 4 ohm, wired to 2 ohms.
And let's say the MTX sub was a dual 4 ohm... that they wired to 8 ohms.
...unless the MTX sub reached more than 4 TIMES the voltage of the Kicker sub, the test would prove the MTX sub to actually be
inferior, if that was the impedence - because that would have been the "break even" point on how much current was flowing.
(and - those impedences may also explain why the JL sub failed just before the Kicker sub - if it had a lower impedence, slightly more current flows

)
Even without ANY of this - the impedence CURVE of the sub plays a role... the impedence to begin with is different at any frequency - with ANY sub... the impedence being highest at the resonant frequency of the sub (as high as 40 ohms, for a 4 ohm sub even!!!).
AND, when you stick the sub in a box - the impedence curve changes, actually! Box volume, box tuning all plays a role... but you can control where the resonant peaks in the impedence curve are.
...so the frequency of the voltage (AC voltage we're talking about here... home AC is 60hz - what's their equipment at?

) is CRITICAL!
Hey, all I need to do is measure the impedence curve (LMS would tell me that), and then send THAT frequency through my MTX sub... and I'd be ensured I'd be sending as little current through my sub as possible...
...and I could likewise target LOW impedence points in the other two subs, and show just how much more MY sub could take.
I hope you guys all understand what I wrote...
Absolutely ridiculous test!