I could see him saying 70 miles without critically thinking about it.
He didn't only say 70 miles, though. He also said it was his "longest day." Yet it's actually only like 35–45 miles, depending where you start and stop. 35–45 miles shouldn't have been a huge day for Kayak Bill. He had "intermediate camps" spaced at distances of 25 miles, so he "didn't have to do those long ones." If 25 miles is an "intermediate" day for Kayak Bill, it's hard to imagine that 35 miles or even 45 miles is his longest-ever day. 35 or even 45 miles wouldn't be my longest-ever day by a long shot, and I'm a middle-aged desk jockey!
In addition, Bill said it took him sunrise to sunset on June 21 to paddle the distance. June 21 is a day with more than 16 hours of daylight. Even I can paddle farther than 35 or 45 miles in 16 hours! Renfrew to Sooke just doesn't make sense as a longest-ever day, even if you grant that he misspoke about the distance.
Now, 70 miles in 16 hours would be a much more noteworthy day—a sustained 3.7 knots, which would be most anyone's contender for a "longest ever day." But then it's hard to reconcile that with the starting and stopping points, which are much less than 70 miles apart. Did he go out and back in the same day? But that's not what he said. It would also be hard to do an out-and-back in the strait, because the tides would jam you up.
No matter how you slice it, it's hard to reconcile the stated distance, the stated time, the stated starting and stopping points, and the "longest-ever day." It just doesn't add up.
Still, you may be onto something with your theory of the misspoken word during the video. What if, instead of misspeaking the distance, Bill misspoke the starting or stopping points? Pachena Bay to Sooke is more like 70 miles—a little more than 70, actually, depending on exactly where you start and stop. Pachena Bay to Sooke would be a much more noteworthy "longest ever day," from "sunrise to sunset," than Port Renfrew to Sooke. I also note that Pachena Bay has a very similar geography to Port Renfrew, making it easy to confuse the two. As a matter of fact, the indigenous name for Port Renfrew is "Pachena"—the cartographers screwed up when they were drawing the maps! Maybe Kayak Bill made a similar mistake and misremembered or misspoke the name of his starting point?
Alex