Talking not about lasers but about Richard Feynman again ... the full quote was printed in his collection of adventures "Surely your joking, Mr. Feynman" in the chapter "Los Alamos from Below".
True, he did not have lasers in mind but look at the original text:
"20 miles away, you couldn't see a damn thing through dark glass. So I figured the only thing that could really hurt your eyes (bright light never can hurt your eyes) is UV light. I got behind a truck windshield, because the UV can't go through glass, so that would be safe ..."
True, ultraviolet light is strongly absorbed in glass, but bright light CAN damage your eyes. I still believe that Feynman was wrong here.
Since the sun's light can damage your light, a nuclear flash might be able to achieve the same. It's all about brightness and exposure time. While a brief look into the sun should be fine, a brief look into a high power laser usually isn't.
Probably the nuclear flash was just for too short a time, that's why nothing happened with Feynman.
Besides ... glasses used for laser protection in the lab are usually specially adopted to a certain laser wavelength. Glasses which keep green laser light out are transparent to red lasers. So protecting cockpit glasses just won't work for all lasers around.
EoD