Application for visa can be denied even if applicant has COE.
This is because, issuance of COE is controlled by Ministry of Justice, and issuance of visa is controlled by Ministry of Foreign Affairs. This means that COE issued by Ministry of Justice is, for Ministry of Foreign Affairs, just a referential document that has been issued by other ministry. From this viewpoint, Ministry of Foreign Affairs can make the final decision whether to permit visa application or not with their own examination.