The two groups who desire to impeach Joseph and Oliver are:
Group A. Those who believe Cumorah is not in New York.
Group B. Those who believe Cumorah does not exist.
Group A includes faithful LDS scholars, educators and members who believe Cumorah is not in New York because it is in Baja, Southern Mexico, Panama, Chile, Peru, or any of a number of other locations, so long as it is not in New York.
Group B includes detractors (anti-Mormons) who believe Cumorah is not in New York because because it doesn't exist; i.e., the Book of Mormon is pure fiction.*
The difference between these two groups is one of degree. Group A seeks to impeach Joseph, Oliver, David Whitmer, Lucy Mack Smith and others on the narrow issue of Cumorah being in New York. Group B also seeks to impeach Joseph, Oliver, etc. on the issue of Cumorah, but seeks to extend that impeachment to everything else they wrote about.
In my view, Group A is a precursor to Group B, meaning that if you accept Group A, it's much easier to also accept Group B.
This progression becomes clear in the following three syllogisms. The first one is the one I posted a few days ago to explain the Moroni's America point of view. The subsequent two show the similarities and differences between Group A and Group B.
Imagine an LDS student who listens to his/her teachers insist Joseph and Oliver were wrong about Cumorah but right about everything else.
People could still choose to disbelieve Joseph and Oliver, but at least their disbelief wouldn't be a logical progression from what LDS scholars and educators are teaching.