Fed does not really "print" any dollars. All the trillions that "exist" only appear in imagination of the people involved and affect their decisions, but they have no paper representation.
What does it matter that the dollars are on paper or electronic, they are still dollars and count the same. They are not imaginary, they are real, even if electronic. When the people says that Bernanke prints dollars, they dont mean that Bernanke goes down to the machine room, gets the paper into the printing machine and presses the on button. By printing money people mean that Bernanke increases the money supply and whether it is in paper or electronical form is irrelevant.
My reply regarding use of "print" verb was to a comment about paper and ink factories. I understand what people usually mean by saying "fed print dollars" and do not disagree with you.