The central difference may be immigrants willingness to work in particular occupations that are shunned by domestic unskilled workers. The occupations that foreign unskilled workers fall into may in some cases actually be complements to the occupations of domestic unskilled workers, and, therefore, the work of the foreign unskilled workers could raise the marginal productivity of domestic laborers, rather than reduce their wages and employment rates as the traditional model predicts.
The primary distinction might be immigrants' readiness to work in certain jobs that domestic unskilled workers avoid. The occupations taken up by foreign unskilled workers could sometimes complement the jobs of domestic unskilled workers, and thus, their labor could enhance the marginal productivity of domestic workers, contrary to what traditional models suggest.