I have little to no issue with outsourcing certain roles, some are more difficult than others and it really depends on the company, etc ect.
Take desktop support. Having an on-site person means your turn-around time between reporting an issue and getting someone at your desk might be very low. With an outsourced partner this might very well mean that your issue gets put into a queue and the person will come on site if needed as soon as possible. This could be hours, this could be days. This usually ends in tears when the director's laptop decides to crap out minutes before a huge presentation and he has to wait 2-3 hours for someone to arrive on site to begin trying to sort it out.
The flipside is systems administration. You don't need to be physically present for many of the tasks. Plenty of tasks can be automated and an even larger number of tasks are not time intensive. Things like "Create a user account", "Add more drive space", etc etc...
However you still need someone (generally Engineers / Senior Admins and/or Architects) to ultimately go "Why the hell have you expanded storage for this server 3 times in the last month?". Your outsourced admin (especially them Indians) will just do whatever is asked of them, no questions asked.





