That's always true of all Sudokus. It follows from the rule "no number can appear twice in the same row (or column)" and the fact that there are exactly as many

That's always true of all Sudokus. It follows from the rule "no number can appear twice in the same row (or column)" and the fact that there are exactly as many columns as numbers to put in them. What the parent was saying, that all rows are a shift of the same sequence, is much more unusual. In case there's confusion over terminology: starting for example with 123456, then 345612 is a shift (and a permutation) while 345621 is a permutation but not a shift.