It only trips people up because the R can't actually move to that square. So if the k were say, a queen, the queen would be safe on that square. The opposing rook would not be allowed to capture it, because they would be putting their own king in check.

If one thinks about chess as if the goal were to capture the opponent's king before one's own king is captured, this makes perfect sense. But sometimes the concept of checkmate muddles peoples' intuitions.