Not true. The Census estimates do a very poor job of estimating population changes within counties, both in terms of differential growth rates (one part of a county might be growing very fast while another part is not growing at all or even in decline, yet Dave's Redistricting would not reflect this) and in terms of race and ethnicity (a racial group may be growing rapidly in one part of a county while continuing to have no presence in other parts, yet Dave's Redistricting must assume equal growth county-wide--metro Atlanta is the most notable place where this is a problem).
Actually, I used Dave's Redistricting App a lot and the growth there in different precincts within the same county are different. I don't see why population estimates must show that each precinct within a county must grow at the same pace, because Dave's Redistricting App. doesn't show this.
The Census Bureau only calculates estimated growth rates based on municipalities (and only based on counties in unincorporated areas, which make up a large chunk of the country), so they don't have the precision to vary population growth across precincts. Similarly, they only calculate estimated demographic changes based on counties.