To help answer this question, a Deseret Morning News article asks (my brother) John Hamer for his analysis. John is a historian specializing in the various scisms within the restoration movement and is the co-editor of Scattering of the Saints: Schism within Mormonism.
In addition to clarifying this issue, John gives some reasonable analysis regarding the public face of Mormonism:
As for whether the move will help erase continuing public confusion outside the Intermountain West over the relationship between Jeffs, his church and the LDS Church, Hamer said he believes there’s an opportunity now to educate people that “there is more than one kind of Mormon. You have fundamentalists and you have the mainstream LDS Church. I think it’s actually helpful to explain that to non-Mormons.”
Denying that fundamentalist LDS members are Mormons “just helps inflame the confusion,” he said. “Since 9/11, Americans are now able to understand there’s more than one kind of Muslim â€” Shiites and Sunnis â€” and they disagree in many ways. In the same way, I think there is the ability for the public at large to understand there’s more than one kind of Mormon.”