You can run up charges by requesting files in any number of public buckets without the AWS keys. The AWS keys don't change the threat model in this situation.
To be clear, I'm no aws advocate.
Yes, it sucks if someone randomly decides to download files from you all day. You should probably set your budget to alert and attempt to blacklist them when it happens. That’s rare, though, and aside from a few cases of actual malice, the convenience is worth the cost.
“Always”