Guh - I wrote a giant post but it took so long the forum timed me out.
In short, it's your Ultimate TV remote causing the problem. Not your VIP1200, the inactivity timer or your TiVo.
I suspect you have the VIP1200 and VIP1216 in the same room, or in a nearby room. When you press the "power" button on your Ultimate remote, it sends a command to the set top to toggle in and out of standby. Also, prior to Whole Home PVR being launched, the "Recorded TV" button if pressed infront of a VIP1200, did nothing, so this seems to back this up as being the cause. -- Why all of the commands you send to the VIP1216 don't get mirrored by the VIP1200 is harder to explain, I would guess that when you press "power" you're in the habit of aiming the remote away from your body and direct at the TV set or set top box - And when you press buttons like CH +/- you hold the remote closer to your body and just aim it in the general direction.
Other thing, unless Motorola moved the IR sensor on the VIP1200 between revisions, it's actually located between the red "record" LED and the menu button, just off centre to the right.
1 - Tent the VIP1200 like a roast! ensure the entire front of the VIP1200 is covered, this includes the first 1/2' on top, bottom and sides. Keep in mind your remote is just an IR flashlight, so even a pinhole could let some commands through.
2 - If the VIP1200 and VIP1216 are near each other move them away from each other.
3 - If you only use your VIP1200 as a receiver for your TiVo, move it entirely out of sight.
I suspect if you try these things, your problem will go away.