We can put this one to bed, further confirmation from RR response to supervisor:
"For the 10-second runoff, the only clock stoppages that “count” are those actions that cause the clock to stop through play (emphasis added) not those for some administrative reason."
Here are the live-ball stoppages in 3-3-2-c through 3-3-2-e that, I'm pretty sure, preclude runoffs for injuries or helmets. (Runoffs for illegal passes work differently.)
Opponent's injury
Opponent's helmet off (no foul)
Team A first down
Team B will next snap the ball
Incomplete pass
Team A ball carrier out of bounds
Backward fumble out of bounds
Score or touchback
Kick down ends
Illegal kick
And it's authoritative that certain "administrative" stoppages do NOT preclude injury and helmet runoffs. So far, the only ones I'm certain of are:
Penalty administration
Any stoppage occurring after the ball is already dead
Here are the ones I'm not sure of though.
Forward fumble out of boundsa) 1/10. A77 is injured. A33 fumbles while short of the line to gain. The fumble goes forward and out of bounds. (3-3-2-e-2) Runoff?
Opponent's helmet off due to foulb) 1/10. A77 is injured. A66 face-masks B99 whose helmet comes off as a result. Ball carrier A33 is tackled short of the line to gain. (3-3-2-e-4, 3-3-2-e-16) Runoff?
Team B awarded a first down but will not next snap the ballc) 4/10. A77 is injured. A11's pass is intercepted by B22 who is tackled in the field of play. B99 was in the neutral zone at the snap. (I think 3-3-2-e-4 is actually the only rule that makes the clock stop here) Runoff?
d) 4/10. A77 is injured. Ball carrier A33 is tackled inbounds short of the line to gain. B99 was in the neutral zone at the snap. Runoff?
Inadvertent whistlee) Ball carrier A33 is short of the line to gain when an inadvertent whistle occurs. (3-3-2-e-6) Runoff?
Other weird ones: Ball becomes illegal, official gets injured, official picks up live ball, what have you.