Sure, you can hire people who don't know anything about testing to do it but I'd expect it to be about as successful as hiring people who don't know anything about programming to do your development.
Testing services are essentially just consultancies comprising of professional software testers.
Testing is a skill with all the associated knowledge, best practice and so on. Professional systems testers with experience are generally people with the right aptitude for testing who've spent years learning about what they're doing. That simply isn't the case for a random individual.
A good tester will know how to develop test strategies, test plans, and test scripts based on the requirements presented. They know how to accurately assess test coverage and progress, they'll understand how and when regression tests need to be carried out and to what level, they understand why tests need to be repeatable and can log defects in a way that allow developers to reproduce them easily, and they know when there isn't time to test everything (which is pretty much always), how to balance the various pressures in ways which have the best chance of maintaining quality (techniques such as striping).
Developers get rightly annoyed when people belittle the skills they have and suggest that it's easily learned but to me this is just the same thing. When programmers ask questions like this showing little thought for what other professionals do or know, what right do they have to expect others to behave differently when it comes to their skills?
Seriously, do a bit of research into what testing really is and what's involved.
Ranty Bit Ends
In terms of the specifics of off-shore testing, it shares many of the same problems as off-shore anything, largely arising from two things: communication and cultural set up.
Communication is an obvious one. I won't go into it much other than to say you need a strategy to deal with it and the main question should be "how will the testers show developers the bugs when the developers are saying they can't see them and wandering over to their desk isn't an option?". Any answer to that question involving e-mail or other text descriptions should be kicked into touch immediately.
Cultural set up is less often talked about but is for me a far more significant factor. By culture I don't mean race, I mean business culture. Most companies I've worked for don't have business processes geared around team members being hundreds of miles away. They don't write specifications in enough detail to allow people to work from them without questioning the person who wrote it (who is now in a different time zone). They operate on the assumption that quick meetings to flesh things out which are missing or unclear are easy to organise.
That's the thing I'd really look at - are your processes really good enough to work with people who can't easily just come and ask a question, and if they're not can you change them so they will work (and do you want to).