The Unopened Letter and Why 'NO'...
At the end of the movie, Everett gave Mary the control of opening or not opening the letter for the core sample results. Her reply was 'No' which brought about the question 'Why did she say this?'.
We must look at the high point of Mary and Everett's conflict to find the answer. That highpoint is the informal meeting at the Mather's house about the law suit she filed.
When Everett walks her out, he questions her on her hostilities towards him. He then goes on to explain that the report isn't even back and that they should cross that bridge when they come to it.
That letter represents 'that bridge'. Everett gave Mary total control over the issue, forfeiting all scientific proof if he was right or wrong. He knew Mary needed that control over her property, which was far more important than what he wanted. By saying no, she is stating that she believes in Everett. It's not that she does believe it's the site but that she believes in the man who found the site.
'That Bridge' that became so important was no longer important. It was replaced by trust, respect and belief in each other which far outweighs any piece of paper.
Besides, why read an analytical report when you can swing? Wheeeeeeeee!!