Always watching: why I wasn’t really alone on my first local solo flight

I called the tower and instead of the usual Alpha to 29, I was advised to turn right on Alpha, left on Charlie and back-taxi on 29 to Echo. I stumbled through my read-back to the tower and cleared the taxiway prior to proceeding. I then noticed an airliner had been pushed back onto taxiway Alpha. The tower then called the airliner and asked, “Who cleared you to taxi?” There was no response from the airliner.