I understand the cause of this is the Joomla IsSafeFile checking in the Joomla core file libraries. This is really a request at some point for a change to Akeeba Ticket System to add a configuration parameter to allow optional override of this behavior by adding the necessary parameters to ATS JFile:upload call. Naturally for most users of ATS this may not be an issue so the default would be to prevent such uploads. In my case I understand the security risks and so all my users of ATS have to be registered Joomla users that have paid a subscription.
Even if you do not think the configuration parameter is something you will implement, it would be useful if something actually caught and displayed the exception you throw of 'COM_ATS_ATTACHMENTS_ERR_CANTJFILEUPLOAD' when the JFile::upload fails in your Attachments model. This currently does not seem to happen as no error message is displayed.
Thanks