Cloud storage just keeps your save file in an external location, in this case, Steam's servers. Cloud storage allots you a certain amount of storage space for you to upload saves, photos, and information linked to your account.
Say if your computer were to fry the next day, you could access your game save on another computer because you downloaded it from the cloud sync. In that way, you don't lose any progress.
The reason he wanted you to restart Steam is in the hope that it would redownload the save for you to access from cloud sync. Perhaps it is best that you leave it enabled.
The same thing happened to me when I played CoOp. The game erased my original save and I had accidentally overwritten any chance of getting it back, cloud sync or no cloud sync. That's okay. I'll play the game over with my friend. I love it.