You're comparing apples to oranges. The Nature paper includes all associated emissions for the food (using "air-freighted asparagus" as an example) while the EPA explicitly excludes non-CO2 greenhouse gas emissions and emissions from production and distribution of both the fuel and the car. On top of that you compare the most efficient car of 2022 in a mixed (city+highway) environment (yes you mentioned efficiency) to the upper limit of what the Nature paper estimates (if all additional energy expenditure was compensated by additional food intake), while the realistic estimate is 0.15 and 0.08kg CO2 per km for walking and cycling respectively.
So there might well be a factor of 10 between cycling to the supermarket and taking your car in terms of GHG emissions. We just can't tell from the sources you linked. And while it's an edgy position to take "I'm just adding to the carbon problem for personal health and entertainment purposes" your claim might well convince people that moving away from a car based society would not have any impact on CO2 emissions. I also think you could make your point that rich people have a way outsized impact without all choices of normal people being exactly the same.