Are you sure?
He's right, it does upload. My housemate started using Spotify a while back and it was crippling the wireless network and internet speed in our flat because of the upload. He now regularly empties the cache folder that Spotify uses and has limited the amount of disk space it can use in the first place, and there's been no problems since.
If you want to stream music, it may be worth looking into standard internet radio streams, if they're allowed. They can tend to be a bit more efficient and there's obviously no upload either.