I keep finding examples where the source and drain appear to be swapped. Is there an error in the attached schematic or am I missing something? Is the battery connected to drain in this example?
Yes, the battery is connected to the drain of the PMOSFET because, contrary to your circuit, the voltage of the USB power supply is higher than the battery voltage.
Without 5V from USB, the transistor gate is grounded, the PMOS is switched on (ideal diode) and the load is supplied from the battery. With USB connected, the PMOS transistor is off and the load is supplied with ~4.6V (5V minus the voltage drop of a Schottky diode). The body diode of the PMOSFET is not conducting because the output voltage (~4.6V) exceeds the voltage of the (fully charged) battery.