I assume they were lucky in that whatever system counts billable requests also has access to the response code, and therefore it's pretty easy to just say "if response == 403: return 0".
The fact that is the case suggests they may do the work to fulfill the request before knowing the response code and doing billing, so there might be some loophole to get them to do lots of useful work for free...
Have often wondered about this in terms of some of their control plane APIs, a read-only IAM key used as part of C&C infrastructure for a botnet might be interesting, you get DNS/ClientHello signature to a legitimate and reputable service for free, while stuffing "DDoS this blog" e.g. in some tags of a free resource. Even better if the AWS account belonged to someone else.
But certainly, ability to serve an unlimited URL space from an account with only positive hits being billed seems ripe for abuse. Would guess there's already some ticket for a "top 404ers" internal report or similar