It's almost certainly not washing past the rings. The high pressure fuel pump sits on top of/inside the valve cover and runs off of a lobe on the cam. When the leak, they leak internal to the engine, and spray a fine mist of fuel into the engine. This fine mist not only dilutes the oil, but it gets sucked up by the PCV system and burned. Because this extra fuel wasn't metered, it creates a rich condition, which is the cause of your rich codes. I'm kind of surprised the dealer didn't know this. I've done several high pressure fuel pumps for this exact issue on Chevy 4 cylinders. Is it under warranty? My guess is that it's an expensive job and they don't want to warranty it.
I don't know whether or not the dealer knew about the part in bold. Likely they are aware of what you are describing. I didn't specifically ask them in those terms, and your description is perhaps more detailed than what a dealer would typically describe to customers.
They don't think there is a fuel leak in the engine, but I'll keep that possibilty in mind.
I got what might be considered a '2nd opinion' today by talking to the most knowledgeable unbiased engine guru I know--a vehicular genius basically. He said the dealer's diagnosis makes sense to him, though he didn't dig in & do a physical inspection.
I'm still researching the issue. It's been working good since I got it back from the dealer but that doesn't mean for sure that I've found a long term solution yet. I've been driving it more & using a block heater.
These below zero temps are getting kind of old but it is winter in Wi.