I think they key is in Peter Ellis' answer; "attempted". When you do sampling properly, you sweat the details of non-response, figure out strata and seek them out, etc. When you decide to do a census, it's easy to ignore those issues, since you're getting "everyone". Problem is, you're probably not getting everyone, but you're not thinking about who you're not actually getting.
There are also statistical issues with extremely large samples (as a proportion of the sampled population). I'm not sophisticated enough to understand them, but at a minimum you have problems with variance calculations. (Packages like R's
survey compensate for such things in large subpopulations of a survey, and that's where I first learned about this.)
As a secondary issue, if non-sample error includes issues due to quality control at various steps in the process, having enormously more data (census) would make it much harder to have the level of quality control that you would have (with the same resources) on a smaller set of data (sample).
Imagine if you had the resources (financial and personnel) that the US Census Bureau used for a census, but you were only doing a survey of 1,000 random adults. I think you'd have much better quality control and much better analysis of the issues involved and of the data itself.