Some devices use CEC (Consumer Electronics Control) commands over HDMI to do things like change inputs automatically when a device is powered on, or "play" is pressed, power on devices, control the volume control on another device, etc.
So, your TV and Blu-ray player both support CEC, and both have it enabled (it is usually a toggle-able option in device settings), so it is changing your input.
Tivos do not support CEC, so it doesn't automatically return to the input the Tivo is on.
You can read more about CEC here, if you are interested:
(the CEC section is about 1/4 of the way down)