With that in mind, all three of those schools enroll more freshman than their "flagship".
Even Idaho State (which you didn't put down under your little 2 flagship thing) enrolls more than UIdaho.
So, enrollment has nothing to do with what is a "flagship" and what isn't a flagship.
It has more to do with the function/mission/purpose/history of the university, and not enrollment, or even the sports they play.
The 2-flagship rule is this. There are two state universities. They both grant numerous PhD's in different fields +, they have these programs/roles/missions:
Flagship 1: Is the oldest public university in the state (usually, but not always), primary purpose is doctorate-granting, liberal arts/comprehensive and professional grad programs, and contain the oldest medical school and law school in the state. The historical critical mass of this school is with liberal arts, med school, and law school. Usually called "University of's _______(insert state name)".
Flagship 2: In 1862, the U.S. Congress passed the Morrill Act of 1862, which established Land Grants to all of the U.S. States (since expanded to U.S. Territories), given land to each state that established 1 public university devoted to the fields of Agricultural and Mechical Arts. The purpose of this act was to provide an education to the common man. Every U.S. State has one of these schools. A number of them became a part of an expanded role of Flagship 1 (such as the University of Minnesota, University of Wisconsin, University of Illinois-Urbana-Champaign, University of Missouri, etc). Other states established a second major state university campus separate from the Flagship 1, thus, becoming Flagship 2. These are like Iowa State, Michigan State, Colorado State, Purdue, Clemson, Auburn, Mississippi State, Montana State, South Dakota State, and North Dakota State. All of these "Land Grant" Universities grant PhD's. They serve as flagships, even if they don't have branch campuses (like Montana State has a branch campus in Billings called MSU-Billings), but even if they don't have a branch campus, they have County Extension offices in every county. In 1913, I believe, U.S. Congress amended the Morrill Act of 1862 to establish Cooperative Extension offices in every county that are affiliated with the State's Land Grant University -- the Flagship of this system. County Extension offices "extend" the university to "every man, woman, and child" in the state. They provide practical education to citizens of the state. These schools, sometimes, in addition to County Extension, have Veterinary Schools, in addition to their Agricultural schools. They are usually, but not always called "_________(insert state name here) State University".
See this link for more on the Morrill Act of 1862:
Idaho State, is not the Land Grant school in Idaho. The University of Idaho is the Land Grant school. U of Idaho follows the University of Minnesota/University of Wisconsin/University of Illinois-Urbana-Champaign/University of Missouri model of a single flagship for the state.
Idaho State was originally a tech school/community college that evolved into a 4 year institution. It was also a branch of the University of Idaho, called the University of Idaho-Southern Branch. It is simply called Idaho State in the same vein as Illinois State or Indiana State, or Arkansas State. None of those three are the Land Grant Universities for their respective states, as the University of Illinois-Urbana-Champaign, Purdue, and the University of Arkansas are for those states. They just simply call themselves "_______State University" because the name was available. I think Illinois State University could've been called Central Illinois University if they wanted to. Illinois State University is a shortening of their former name of Illinois Normal State University, as they were a teacher's college, hence the name "Normal" in their name.
So the 2-Flagship rule has nothing to do with a name, but with the function/history/mission and peership (across the country) of the institution.