That is good general advice. However, there are always a few exceptions, depending on the specific board positiion. Either your opponent forces you to move one of your castle-side pawns, or in some rare cases you can attack on the castled side (but this doesn't happen too often).
Also, later in the game, you often need to move one of these pawns to prevent a possible back-rank mate situation.
A solid chess player gave me this tip. Is there any truth to it?
He said that the pawns in front of the castled king should not be moved. After moving the center pawns to get center board, the only pawns that should be advanced are the pawns opposite the castled king. Move the pawns on the castled kings side during the end game. Move the pawns on the other side at the beginning and middle game. Is this solid advice?