Niklas, by user I mean the person (i.e. email address) who has either run the script manually or scheduled the script. So if you run scripts on different AdWords accounts, but use the same email address to log into them, you will hit the limit if those scripts make more than 20,000 fetches total (per day). If you find yourself frequently running into these limits, you will want to schedule the scripts with different email addresses.
Cheers,
Alex