You are wrong. "Dual intent" of H1B means that you can get it while having an application for a green card on your behalf (thus expressing an immigration intent). In general nonimmigrant visas are denied with such an intent but H1B and few others can still be issued.

But you can apply for a green card with any visa or no visa at all, there is no visa requirements on a green card application (I140 if we are talking about EBGC specifically) what so ever.