Wrong again. They didn't want government representation to be on the basis of only the free white populations in the states, as counted in the census, since the free white populations of some rural Southern counties was much much lower than that of the enslaved populations.
The non-slave states would always have far larger representation in the House than the Southern slave States, because nearly all of the northern population would be counted, whereas nearly 1/3 of the population of the South would not be counted and those states would have fewer representatives in the House.