Accuracy has little to do with being a primary source. I'd consider census data as primary, because even if the data includes interpretation, it's not historical interpretation; it's someone making sense of the situation they were in at the time, and as such is much like manuscript correspondence. The example of which I'm thinking is the 1851 census where my great-great-grandfather, Christopher, is described as a 'farm servant'; but his employer, described as a farmer by the clerk who made the initial entry, is then downgraded (as are other farmers in the area) on the grounds (explained in a marginal note) that although possessed of substantial acreage he only has a small proportion of it in cultivation. My reading of that is that the overwriting senior official thought that the agricultural depression was the fault of farmers choosing not to be industrious; but I have no evidence for that. The overwriting clerk's decision is still, to me, primary evidence because it's a voice from the time.

The birth date evidence in the census is still primary because it's evidence for age, not birth year; the conclusions that people make about birth years from the evidence are, however, secondary.