Specimens vs People

According to Covid Tacking Project's web site the following states record specimens tested as opposed to people tested in the state's daily "case" count. 

Alaska
Arizona
California
Connecticut
Florida
Georgia
Idaho
Illinois
Maine
Minnesota
New Jersey
Oklahoma
South Carolina
Texas
Virginia
Wyoming

As the web site points out under each of these states :

 _____________reports specimens tested instead of people tested. Because some people may be tested more than once, this number is probably higher than the number of people tested. 

Considering that this list of states includes the three of the most populous states. These states currently account for over two million cases or 52.5% of all reported cases in the United States. How many of these specimen tests are of a previously tested positive individual? We have no way of knowing. How many "cases" are duplicated? Again we have no way of knowing. If only 10% of those tested in these states are duplication's then there have been a quarter of a million less "cases" in the United States than reported. 

The number is probably far more.