What did the woman in the boat mean when she said "He doesn't ROW"?
Solution 1:
The game is a cycle but with many varying dimensions. As Elizabeth says at the end, there are some constants and some variables in each cycle. Apparently, one of the constants is that Booker does not row the boat to the lighthouse. So it's not that he can't row any boats, it's that he does not row this boat. To put it in the Luteces' terms: he did not row, doesn't row, will not row the boat.