Nope. If you have the book you are good.
Did you give money to the town mayor?
Yes, both before and after getting the book. Second time got me a Tear Of The Sun. Funny thing is, after saving and loading my game, I tried to enter the cave again, but it still said that the cave is flooded. After that, I tried to pay the mayor again, and he gave the hint again, after which I could enter with no problem.