I agree that Mitt likely has no idea about this and isn't doing anything that most of his opponents wouldn't do too. If you visit any of the left leaning sites right now, they're all hammering away at this topic as well as the fact that the Olympic Teams under his tenure had their uniforms made over seas. -As if he was personally on the team that sourced vendors for their uniforms. It's silly.
Mitt has chosen to pay the opportunity cost of being hands off with his money for a bit while he gambles on a bigger pay off. The dollars may not matter all that much, but there will be plenty of payoff from this campaign in name recognition, a place in history and probably many other things. He might actually have a pretty good idea where his money is going, but needs to keep a nice veneer of plausible deniability.