Look, I am going to speak from a customer point of view since I am not a hosting company, neither am I working for one.
When it comes to tech support, I don't care where it comes from, as long as issues are solved quickly and in both professional and friendly manner. There is nothing worse than unreachable support, that is impersonal or does the bare minimum. In-house support will tend to care more. However, it is because there is a popular notion that outsourced support automatically means the one coming from far abroad (India, etc), where quantity always seems to overcome quality. I can say through experience that in most cases that's unfortunately true, whether you are working with a technical person or any other freelancer. So I don't expect anything different anymore. If you are set on outsourcing your support department partially or in full, at least look closer to home. For example, here is one that is currently advertising on our forum: <URL removed: wrong service category provider>
I have no direct experience with PlatinumServerManagement, but it is an example of an affordable outsourced support company with an all U.S. based personnel, which is impressive to me. In fact, I've known about them prior to them becoming an advertiser here for that same reason.
There is nothing wrong with outsourced support, in my opinion. Just make sure to have someone that will treat your customers as if they were your partners. And don't make the price alone the decisive factor.