I think we over simplify things sometimes. I'm no expert, but we often like to think of things in terms of timing and what happens immediately after a workout, etc. It could be that arginine hinders the release of GH, or it could be that arginine alleviates some issue that means we require less GH to get the job done, or makes GH more effective. I'm not saying I'm right, just saying there are other possible answers to this.
Either way, arginine isn't the best pump enhancer as others have pointed out and if it concerns you, there are plenty of Pre-W without arginine in them. Of course, taking Citruline is a better way to increase your blood levels of Arginine than taking arginine itself...so not sure how citrulline wouldn't have the same effect.