Does your experience include reading Publication 501, pages 16 & 17.  If it did you would clearly see that unwed parents can choose which parent claims the child.  Now the lucky parent has to claim all the tax benefits available, but this means the mom in your case has every right to claim the child and EIC for the child.  She probably did not qualify for the Head of House, but as Susan pointed out, she probably did not need that status.  And legally, parents can switch back and forth each year as long as the lucky parent claims all benefits.

So read the examples on those pages and enlighten your experience. 😀