I was searching for something else, but I felt compelled to answer this after 3 years
The keyless entry/keyless start is a convenience so you can walk up and unlock the door and you can start/drive the vehicle without ever taking the key out of your purse or pocket. This process requires a little bit of power from both the vehicle and the key to establish a wireless communication.
If the truck is dead: The physical key will gain you entry to the cab and under the hood to repair the battery. You won't be starting the truck with a dead battery, so there's no point in having a physical key to start the truck. Jump or Replace the battery and the keyless system will go back to normal.
If the fob is dead: The truck still has power to send out communication, but the key cannot respond. As a backup, the key has a RFID coil inside that works exactly like an HID/proximity keycard. You will still be able to enter and start the vehicle by holding the key/fob it near the Start button. For the record, the RFID is located in the base of the physical key, not the fob itself.
Proximity/RFID only has a usable range of about 2-inches (usually). RFID works by the reader constantly emitting a small electromagnetic field. When the RFID comes within range, the EM field produces just enough energy to power the RFID and send a signal back.