If they have electronics on board, they are highly likely to require the right supply polarity.
Yep, that's what I was thinking.
From what I read in 'Silicon Chip' magazine, these high intensity white illumination LED's have different characteristics to the small red/green types. They require higher voltage, and a constant current supply for decent intensity and life. Not just a matter of running a few in series from a nominal 12V supply via a current limiting resistor! There are various LED driver chips available, which can run MOSFET switching transistors in a buck/boost power supply so as to use that wide input voltage range. In wholesale quantities, these chips run about a dollar...
I wasn't thinking of a wide tolerance of supply voltage, just a design which had the same voltage tolerance as an incandescent globe - in other words, very little tolerance.
Well, they do have a bit of tolerance, but the light intensity drops dramatically under nominal voltage, of course.