Yeah, that particular part of the campaign has GRRM’s thumb squarely on the scales, because it has to happen that way in order to set up Robb’s decision to go for Jaime or Tywin.
I mean, it’s technically possible to take successive castles by surprise – but it becomes increasingly unlikely with each castle, because word spreads fast. And it’s absolutely possible to ignore castles as long as you’re willing to live off the land and cut yourself off from supply lines, but that doesn’t seem to be what Tywin was doing, since these castles are described as fallen not bypassed.