Again, research. That's why you get to know the company you're putting your servers and customers into. There's plenty of companies that are not fly by night companies that charge reasonable (around $100/month) rates for management / support and can do the job well enough.
It's all about who you use here
Outsourcing the wrong company will be bad for your business, but even choosing a good reputable company , all it takes is them to have a rogue employee that can still sell on your customer details. You have also got to have someone that can visit these companies and train them in the ways of your business.
It is also hard to monitor these companies, so it is always best to have support etc. inhouse where you have control.