I'm guessing that there is a difference between "offshoring, while still having the offshore people picked and employed by you" (let's call it "pure offshoring") and "offshoring and outsourcing to a local company" (let's call it "outsourcing to offshore").

With pure offshoring, you do have control over who you pick, what their mode of work is, whom to fire, etc.

With outsourcing to offshore, the local company hires people, usually on the cheap, to only just fullfill your contract and no more. If people underperform, you may complain, and maybe they'll be moved to a less prominent and visible role, or maybe they'll be shuffled to the next customer of theirs. So things will be bad, because it is not in the interest of the local company to do one iota more than necessary. And you'll still have to have your own QA, architects, etc., to make sure you at least get what you paid for.