That's not the only reason their putative importance is exaggerated, though. It is also exaggerated because the swing states are whiter and blacker, and less Hispanic and less Asian, than the rest of the country is.
The following table and graphs show the total population racial/ethnic distribution in the 12 states Real Clear Politics lists as toss ups and the total population racial/ethnic distribution in the other 38 states plus DC.
While Hispanics are the largest non-white minority group in the country, they're heavily concentrated in electorally safe states like Texas and California. In the states most likely to decide the outcome of the general election, blacks outnumber Hispanics (in addition to being more likely to vote than Hispanics are).
Florida is the swing state with the largest number of Hispanics, but Florida's largely Cuban and Puerto Rican Hispanic population cares less about Mexican immigration into the US than the country's non-Floridian Hispanics do.
Proportionally, the non-Hispanic white population in the swing states is a little more than a decade 'behind' the country as a whole. The 2016 swing states are about as white as the country was in 2004.
Appealing to Old America looks to be a better electoral strategy than Hispandering to New América is.