There’s always that one guy who comes along 8 years later and adds his two cents. Today it gets to be me.
The evaporative emissions system circuit does indeed connect to the fuel delivery circuit. Vapors from the vapor cannister are carefully vented into the intake manifold when the ECM detects certain conditions. On many cars, they are dumped into the intake manifold past the sensors. If the purge valve malfunctions, it will allow unmetered air into the intake manifold. Just as with a blown intake gasket, this will result in unexpected readings by the oxygen sensor, triggering a P03xx code. A purge valve is more likely to malfunction when the gas cap itself is malfunctioning, because that affects the sealing and pressurization of the fuel system. The fact that he mentioned it happening when the fuel level was a certain way supports this; the EVAP system does not run when the tank is near full or near empty, or when ambient air temperatures are very high or very low.
Note that an OBDII system only triggers a code when certain conditions are detected. They cannot diagnose a fault. That is why nerds with handheld scanners have not completely replaced skilled diagnosticians despite over 20 years of OBDII in cars. Ask any decent mechanic, and they will tell you that when they get a P03XX code that faults the O2 sensor, they still check the freeze frame data and often see anomolies in other systems that lead them away from the O2 sensor as the culprit.