I agree with Jfrazier... Every time I have called, the people on the other end of the phone are extremely helpful and patient. (Have not experienced anyone from the Philippines to date).
As far as closing a ticket without customer approval... No way! I understand the need from tracking metrics and determining call processing efficiency, but the customer has the final determination if a case should be opened or closed. Generally, in working with other vendors, if I think a problem is fixed, I will tell the tech on the other end of the phone to keep it open for 24 hours and close it if I have not called back. They usually have not problem with it and the process works well.
One Exception: If you try to call me over the course of a couple of days and I don't get back to you... close the ticket.... I'll reopen if I need to.