That's the tough part with the Narrows. You need a back country permit in advance, you have to plan your travel in advance, and a high river can wipe out the best laid plans.
Yep, My son was down in a slot canyon for a school project earlier this year when it started raining, He said it was amazing how fast the canyon filled up. Fortunately they were at a spot where they could get up and out quickly so they never were truly in danger. He said he never had been so scared in his life as when they noticed the water rising.