If you were right in your logical conclusion, then a couple couldn't have sex when the woman was not ovulating or post-menopausal, could they? Does anyone argue that? No.
That said, though, I agree with your other point that the whole reason the left is bringing this up is to redirect the conversation. We shouldn't take the bait--because bait it is. Never let the enemy choose your field of battle. If they steer the conversation to birth control, steer it RIGHT BACK to abortion and the first amendment.
Oh how magnanimous of you (and the church btw) for granting this exception.