Who do they think runs the church they belong to?

this was a head line in the Provo Daily Herald:
Letters condemn church's support
Jennifer Dobner - The Associated Press

and this was the story:
SALT LAKE CITY -- A group of LDS members who support gay marriage said Thursday they plan to deliver 300 protest letters and a petition to church headquarters.
The group signingforsomething.org disagrees with The Church of Jesus Christ of Latter-day Saints' support for California's Proposition 8, which would ban same-sex marriage in the state's constitution.

"I think it's important that the leadership of the church knows that we have varying opinions within the church and that we're not all in lockstep behind them," said Andrew Callahan, a church high priest from Hastings, Neb., and a member of the group.

and the story went on. I wonder if, as members of the LDS church, they believe that the prophet is running this church or that it is run by the LORD. Do you think if they believed that it was run by the LORD that they would deliver their petition to him? If they don't think it is run by the LORD, why are they still members?