I share your parent's skepticism. It seems obvious that cars sold in the US are not averaging 37 MPG when the average car is roughly a RAV4 that gets 22/29.(EDIT: It occurs to me that the RAV4 may be classified as a light truck -- even so, I can go pick a passenger car...)

As far as I can tell taking a quick look at your links, the difference can be in two things. First, these are fuel economy standards companies are expected to hit, and not reporting on whether they hit them or missed and paid penalties. Second there's the phrase "Assumes manufacturers fully use low-GWP A/C refrigerants credits". Apparently fuel economy numbers are boosted by these credits--actual fuel economy isn't the same thing, it appears?

(EDIT: Overall fuel economy for cars and trucks combined was 24.8 mpg in MY2015 [1])

[1] https://phys.org/news/2016-11-average-fuel-economy-high-mpg....