You don't take off with 30 degrees of flaps though, fortunately.

Correct. This was likely a flaps 15° (or maybe 20°) departure (being a heavy departure).

262 is still too high for either of those flap positions according to the above list. So while you may be correct with your comment, it is pretty much without point???

Edit: At least for the topic of this discussion. However, I'll now be able to win a bar bet when someone aks what flaps position for a heavy take off of a 777 would be

Sure. The question becomes "given an airplane that's had a limit airspeed exceeded by about 22% (so aerodynamic loads typically less than 1.5x the placarded limit), what's then the safest course of action for a crew who just minutes ago demonstrated that they were incapable to perform an uncomplicated, utterly standard takeoff procedure?"

Do you want them declaring an emergency, dumping fuel, flying around at night, and coming back for a max weight emergency landing? Or do you want them continuing the flight, sending someone back with a flashlight to look over the wing trailing edge, and continuing on as normally as possible to DC? If my butt or a family member's butt is on that airplane, I don't want these yoke holders trying to figure out and execute the emergency procedure after flunking the standard day one of flight school procedure, while flustered from almost milking themselves, and knowing that they’re looking for a job in the new year. Take a few hours; paint a magenta line all the way to DC and fly it.

The 777 has a flap load relief system and should retract the flaps at 216 knots. Don't know if it works this early during takeoff.