Both explanations are essentially the same, and both are correct, they're simply worded differently.
Try to think of it a bit like the standard deviation. We derive a parametric estimate of a standard deviation by dividing the sample variance by n-1, because the sample will necessary underestimate the amount of variance in the population. If, however, we have sampled the entire population, the correction is unnecessary and the standard var/n standard deviation statistic is perfectly suitable.
Same with regression. Samples will consistently produce a parametric R2 estimate that is inflated, so the adjusted R2 is used instead. If, however, you regress data from an entire population, it is no longer necessary to adjust the R2 coefficient because it is no longer biased.