That fix brings up an interesting distinction. When I read what Steve wrote I heard him talking about the exercise of authority. But what he literally said was about the possession of authority. The claim, literally, is that the wife is the source of authority, which she voluntarily surrenders to him.
And a lot of times when people talk about this topic, 'you can't tell me what to do', 'submission must be voluntary', 'its wrong to make her do something'...they're communicating the practical idea that her submission is contingent upon her voluntary participation, yet the underpinning idea/theory is that he actually has no authority over her. Voluntary submission is't submission (i.e. being in subjection to another); its cooperation. If he has only the authority she allows him, then she's actually the source of his authority and we've inverted the headship of God->Christ->man->woman; which technically makes the woman into a god (no surprise various features of woman worship creep in; its a temptation that goes back to the garden).
An analogy... Taxes. No one can 'force' you to pay them. Payment requires you to choose to comply. Yet that choice does not mean they're voluntary. Taxes aren't voluntary, they're compulsory. If you don't pay there will be consequences (fines, arrest, imprisonment). The authority for taxation doesn't come from your voluntary cooperation, but from the sovereign authority of the governing institution which you fall under in the human hierarchy.
Likewise in our day, even though the god of this world has given the wife a lot of leverage with which to fight back against the husbands authority, he still has it (1 Cor 11). So far as tools go, the balance is tipped way in the wifes favor. But this doesn't mean husbands are at the complete mercy of the wife. For the exercise of our authority is consistent with her created nature, what she deep down wants; often even when she's resisting it. He can still enact various consequences for her disobedience or kick her out if she won't comply.
Is it authority if it cannot be exercised?
As a matter of principle yes, Men have authority from God. The more appropriate question is, are we able to exercise it? Is there a point where it can be so restricted so as to be null? I don't know. It is a fair question given the extreme degree to which men have been dis-empowered in this day.
Rulers of this world have authority to do many things, but they're not always able to exercise all of those for practical reasons; at least not without severe enough consequences that they stay their hand.