They are very clear that you should NOT do it on shore. You're supposed to go to the expedition folks and they'll shuttle you back to the ship to use the bathrooms there. The ship does not dump into the water, as many do, but stores it to be pumped out in port. (At least that's what they say, I certainly hope they're not lying about that.)

So, I was careful about how much I drank before a landing. But, the longest we were on shore was just over an hour. Even with the zodiac ride there and back it was under 2. So, we didn't have a problem. I did see some trips back with only a few people in them, so it might have happened to a few folks.