I don't necessarily disagree or agree with easyhostmedia's response. You have to look into this subject in two different mindsets.
1. Look into the perspective of Outsourcing Support vs. Not.
If you choose not to outsource your support, you could still be left with headaches. There's people in every country that will try to hurt you or be a rouge employee. You can look at this BBC article of a Indian Call Center although don't let this make your decision for you. I'm sure i can find similar articles of US call centers or employees with the same behavior.
You can never rule out EVIL it's everywhere.
2. Outsourcing Support is cost effective way to not only provide 24x7x365 day support but assist you with many tasks you couldn't afford to be completed in other countries.
I'm not saying you should outsource your support or not, all i'm saying is if you screen anyone properly and do your research, RESEARCH is key. You could end up with a good outsourced company.
Don't put all your eggs in one basket, find a company you like and research them. Find their customer reviews, are they BBB accredited? What other companies use them? What's their mission statement? How do they secure your information?