Differential thrust with one inoperative thrust reverser isn't a big deal. It's something to be aware of but not something to be afraid of.
A damp runway isn't contaminated. With contaminated runways, with snow, sleet, slush, on the runway, you need to be very careful using differential thrust. The MEL may prohibit operation into contaminated runways with an inoperative thrust reverser.
It's hard to understand how an engine power was advanced enough to cause a runway excursion. It happened. Professional pilots are puzzled since the Captain's hand is typically on the throttles ensuring that they're at idle and remain at idle.