Unfortunately, because of the way the restrictions on elevation are, users must accept a prompt for programs to get admin rights. Because the task scheduler runs as a system service, it has more freedom on what it can do, which includes creating elevated processes and executing as different accounts, all without user interaction. You COULD, of course, turn UAC off, but that's generally a bad idea.
Bottom line: The only ways I know to get automatic admin access are disabling UAC and using the task scheduler. If anyone knows a different way, please say so. I would love to know also as it has been a problem for me in the past.