If I try to retrieve an issue via the SOAP api (Method getIssue), and the issue does not exist in the JIRA database, a RemotePermissionException is sent back to the client.

The Javadoc at https://docs.atlassian.com/software/jira/docs/api/rpc-jira-plugin/latest/com/atlassian/jira/rpc/soap/JiraSoapService.html#getIssue%28java.lang.String,%20java.lang.String%29 says:

RemotePermissionException - If the user is not permitted to perform this operation in this context.
RemoteAuthenticationException - If the token is invalid or the SOAP session has timed out
RemoteException - if the issue does not exist or your dont have permission to see it

The Javadoc and the actual implementation do not behave consistently.