a somewhat similary situation...
my local Wendy's no longer has a live person at the drive-thru window to take your order. well, not exactly... when you drive up to the menu board, the person on the other end of the mic/speaker is actually sitting in a call center two states away. they take the order and its prints out at the Wendy's kitchen. when I drive up to the window, I pay and pick up my order... the manager tells me that it's much easier this way.(probably cheaper too?)
well, at least not it's not a call center in India!
come to think of it, when I pick up a hotel phone and dial the magic one-number-for-everthing, am I actually speaking to someone who is physically inside the hotel I'm staying at? Seems to me that they can also do what Wendy's is doing, no?