I don't like the way they worded that because castling has nothing to do with whether or not doubled pawns are a weakness. The biggest factor is how close we are to an endgame and especially just a King and pawn endgame situation. In the endgame, the doubled pawns tend to be very weak and will probably cost that side the game; when play is still in the opening/middlegame stage, then there is potential dynamics to justify the doubled pawns and they might not be as weak.
I guess their implication is that castling is further into the game and doubled pawns would be weaker, but I really don't like this wording because castling has nothing to do with the fact.
Here is a video I made which might be interesting for you though:
During a lesson about the Italian Game by the site, I noticed in one of the challenges notations the quote "Black hasn't castled yet, so doubled pawns aren't an issue." Why is that? What if I need to castle right at the next move?