Amazon is responsible for making a reasonable effort to prevent anyone unauthorized from doing anything to an account. Swap "shut down" with "read personal information tied to account" or "upload a heinous webpage to the AWS server," whatever.
This is not one of those "by any means, achieve the ends" type scenarios.
Presumably because that only happens when it crosses a threshold dollar amount, and $0.80/month isn't enough to get it over that threshold.
(That price is too small for there to be a running instance; it's most likely for storage belonging to an instance that was shut down, such as a 16GB EBS snapshot. It is reasonable that Amazon would be very careful about deleting that.)
That's not particularly relevant to the question of whether a fraudster should be able to shut down your account simply by offering to pay the current bill.