You are actually mistaken yourself. Green cards do not depend on non-immigrant status, being an immigrant visa. Thousands of people (at least 50000 DVs + CP EB and FB) get these visas, arrive to the country for the first time and become LPR without using any non-immigrant visa.
You are right.. I missed the diversity quota completely. It is not available for some and open for others. I had friends from West Indies (Trinidad and Tobago) come with green card.
Not just diversity, most immigrant visas can be obtained through consular processing (CP). You don't need to be in the US for any employment or family based immigrant visa. I am not a lawyer but I imagine only asylees need to actually be in the US for their greencards but they don't need a non-immigrant visa as well.
