I think you missed the point when you spoke of only one side of the Martin's Cove story being told on a Mormon-owned site (HCN, 9/30/02: This land holds a story the church won't tell).
The issue of a "holier-than-thou" attitude that led to movement from New York to Ohio to Missouri to Illinois to Utah is peripheral at best. The pioneers in the Martin and Willie handcart companies were not running from anything. They were marching toward their Zion, no matter what led their church to Utah.
And I see no reason why the Mormon church should be required (at Martin's Cove) to tell the story of how the Nauvoo, Ill., city council-sanctioned destruction of a dissident press contributed to Joseph Smith's death the next month at the hands of a mob. There were no former Nauvoo residents in the ill-fated handcart companies.
Another (relevant) side is definitely lacking at the Martin's Cove site, but you missed it. This is it: To what extent was Mormon leadership responsible for the deaths in the Martin and Willie handcart companies? Many have blamed Brigham Young for leadership decisions that led to the deaths.
Take those other (legitimate but misplaced) protests to other church-owned sites like Carthage Jail or Nauvoo, Ill., or Kirtland, Ohio, or Independence, Mo., or. ...