Val Kilmer even moved in with Kurt Russell while they were making the movie so that they could work an “extra 20 minutes” on the project before crashing out for 4 hours and then getting up to hit the set.
Kilmer doesn’t explicitly say that Russell directed the movie, but Russell has said in the past that he did.
Val Kilmer starts off his blog post by saying that Russell made the movie happen.
Kurt Russell basically said the same thing when asked about Tombstone in a 2006 interview with True West Magazine.