So, my question is how does the restore not complain about the fact that a full backup in the middle of my Trans Log schedule has been done without the COPY_ONLY option?
Any problems pertaining to backup 'rules' will be raised by SQL Server during the backup process, and reported by SQL Backup. SQL Backup by itself does not perform any validation of the 'rules'. E.g. if your database is running the simple recovery model and you attempt to back up that database's transaction log using SQL Backup, it is SQL Server that raises the error, and SQL Backup simply reports it.
In your example, there is nothing wrong with taking a full database backup. Neither SQL Server nor SQL Backup can ever know that only full backups taken by your scheduled jobs are considered 'valid', and other other backups should raise an error during the restore process.
If you need to know when full backups have been made by other users, you can refer to the backup history tables, as described here