I've heard countless times from men that I am "simply" a front for a male owned company who will "really" be doing the work. If I am not a front, I will be according to them.
I know another female engineer running her own company. She's experienced some of that, too, and she ignores it just as I have. Her comment regarding her experiences and being a DBE, "You still have to be able to do the job. So in the end, it doesn't matter."
Larger engineering firms sub work to smaller engineering firms for a lot of reasons. It happens for some surprising reasons, such as risk avoidance. I've worked with engineers who refused difficult projects. For some men, it's OK for a male owned company or a NYSE firm to sub work to another male owned company but women or other minorities should not be allowed to participate.
It's intriguing that some don't understand how business works. Often work is subcontracted to whatever company can or will take it on. Often work continues getting pushed down to some very small companies doing the work.
I think the deeper issue working in men who don't want women in the sandbox is fear. Fear that they can't compete. Fear they'll lose ground. Fear of a stacked deck that they didn't stack.
I've battled those same fears in various situations. It's an ugly, base, raw emotion to deal with. Ultimately, I try to recall that God is not running a zero sum game, which is obvious in view of history. God will take care of me just as He will take care of others. He has a place for me, which I should not fear.