I have had the same problem with one of their bulbs. I have yet to pull it to take a look but was thinking more along the lines of a short across some of the electrical leads. If you look at the LED towers, at least mine have exposed contacts on the tower itself and I was expecting to see water or corrosion or both shorting out some of the individual LED elements. If my bulb was not seated properly or there was a break in the seals, then I could see that happening and half-expected that to be the case. I have yet to confirm this however.
The theory given by autolumination doeas make sense however. If you have your bulbs on from the moment you turn your key on, then turn the key to start the vehicle, your vehicle is dropping and surging voltage pretty wildly. Stick a voltmeter across your battery terminals as you perform that action and in most vehicles you wil see approx 12v with no load, drop to as low as 10v when the starter kicks in, and then up to the nominal 14.4v when the engine starts up and revs the alternator up to speed. All that is assuming everything is functioning fairly normally. Thats a pretty wide drop then surge in whats typically 5 seconds or less.
That being said, these are being sold as automotive bulbs and SHOULD (one would think) be designed to handle surges common to automotive applications.
His test of removing the bulbs and testing them with a known good 12v power supply proves nothing except that some of the LEDS have been blown or not. His fix of inserting dimmer (a simple pot)or equalizer (prolly a simple resistor/capacitor/diode combo) does make sense if surges indeed are the problem, however it will not fix your current bulb.
If you choose to replace the bulb and not use one of his fixes, another fix would be to ensure the LED lights are not turned on as the engine is started, but that would be a relay/switch combo which could prolly be rigged using mostly existing wiring. Not sure.