500 lumens from a single AA?
Engineers ARE making some impressive advances in DC circuitry. However, as you say (paraphrasing) 'The Laws of Physics STILL Apply.'
There are some really nice, even smaller, 600 lumen flashlights running off CR123 sized batteries.
The key unmentionables are that as the LED heats up exceeding the ability of a metal case to dissipate the heat, the lights auto-downshift to lower power modes. And these things should be looked at from the standpoint of Ampere HOURS and the ability of an alkaline battery to push necessary current (use a Li-On) and life of about 2-20 minutes at highest settings. LED lights can provide several days of runtime at low settings (say a candle's brightness), and for only seeing in total darkness VS reading or examining for a few seconds, that is adequate, even preferable. Lastly, they don't mention the color of the light, which impacts its usability as much as brightness; the whiter the better (look for 4000-5000K).
But, this is a small plastic package, not meant for every day use. It is a $3 flashlight - replace it with a $20 flashlight, USB-rechargeable Li-On battery and toss in a foldable solar charger...