Rip,
Their quality isn't the question. Accountability is. If one of your outsourced contractors took private information and misused it, the most you could do is terminate the contract, file a complaint in world court (haha like that would do anything) and tell your customers *oops sorry*.
Where's the accountability? Without accountability, you're relying on human nature and even people who don't hate America with a passion are still human, and people sometimes do bad things. Toss in the possibility of a contractor getting infiltrated, and now your entire company and customer base is at risk.
Someone I know found and helped the FBI catch an for-real no kidding international spy in his company... Because it was in the US, there was accountability.
Rip, if you take full responsibility for everything that happens at the outsource contractor, then go for it. If you can't answer that call, then maybe the contract should have stayed in-house or in-country.
Heck, if it's outsourcing the making of shoelaces and there is no proprietary technology in those shoelaces, then by all means please outsource. But if that contract is something even as simple as managing a contact database or handling ANY private or corporate-confidential information, someone need to be accountable and I say it ought to be whoever approved the contract, fully and personally.