The idea that they had an "extremely friendly relationship" is a bit overblown I would say, and since it's mostly a modern invention, contemporaries don't really say anything about it. I've written a bit about Saladin's relationship with Richard (and other kings) in some previous answers:

When Richard the Lionheart and Saladin entered into treaty negotiations, would they both be there in person and speak or was it down on paper?

What did Saladin think of Richard the Lionheart and Baldwin IV?

During the Third Crusade, both Conrad of Montferrat and Guy of Lusignan opened negotiations with Saladin for support of their separate claims to the throne of Jerusalem. Why would either of them seek support from Saladin, a man fully intent on destroying the Kingdom of Jerusalem entirely?