Only now people have realized that English is different from Hinglish, Chinglish, Finglish, Singlish and cost-wise it is okay (economical and easier) to hire "barely educated" within the States than to train someone in Asia who would jerk the consumer experience quite often. I think both situations are completely different.
For example, Taglish is Tagalog with English mixed in (or vice versa) and you'd be hard-pressed to find any call center in the Philippines that relies on Taglish.
So you are saying cost is the reason to outsource and because of cost that Aegis is hiring US workers to avoid paying for English training, which means Aegis is outsourcing English speakers to the U.S.
The U.S. outsourced call centers and India is outsourcing English speakers. Same thing. Indian companies (Aegis) are hiring Americans = outsourcing = American companies hiring Indians.
I'm not sure why you think it's different.
Hinglish may not be English, but C++ is C++, algorithms are algorithms, intelligence is intelligence, but INR is not USD. Outsourcing is (quasi-)arbitrage!
The accent is only an issue if the job involves trying to please the http://www.peopleofwalmart.com/photos/top-rated/.