It is not so. The results from 'Self Check' are not at all any kind of official document or a record of the applicant's work authorization status. This is so because, many things may have happened to change an applicant's status. Some of these changes are for example, a change in citizenship status, or the expiration of an immigration status, etc.
It simply means that there are individuals who are authorized to work and those who are not. While natives of the USA, green card holders and some few others are authorized to work, others who do not have a valid kind of visa to work are not eligible.
This is a category of visa through which some businessman/entrepreneur, etc. invests money in an enterprise and creates jobs for US workers.
This option can be availed of by 'individuals of extraordinary ability', or by those who have been granted a 'national interest waiver'.