My FTAnalyzer program treats ABT 1860 as being 1859 or 1860 for precisely the reason Peter mentions. All bar the 1841 census takes place in the first 100 days of the year. Thus around 30% of people on the census with a year abt 1860 will have been born in 1860 but around 70% of them will have been born in 1859 and have yet to have their birthday in the census year.
Thus on balance of probabilities you should consider it likely that the year is out by one from what most sites show.
Thus on balance of probabilities you should consider it likely that the year is out by one from what most sites show.