That was my first reaction - just lie to 'em.
In a similar vein, the VA routinely asks me if I am depressed. Never have been, in their context, but if so, I would lie there too. I understand that if you respond with a "yes", you go on the Brady list as a "potential suicide" and will therefore fail the background check. Try getting that removed.
I routinely get asked that question as well when I usually visit my primary doctor. And as usual I answer no as I too realize as you do what an affirmative reply means no matter how I'm feeling one way or the other.