Yes you can be questioned without being read you Miranda Rights. However the statements may be objected in court due to your boyfriend not being read his rights. If statements are at the heart of his case it may matter. But if he is convicted of a crime simple evidence may suffice regardless of the Miranda rights.
The police are not required to Mirandize. If the person is arrested, or is a suspect in a crime, the police will Mirandize him/her. Generally, however, in order to protect all parties, everyone is "read" a version of their Miranda rights before questioning. It is not a requirement, however,
Police may question anyone they like without reading them their Miranda rights. Only when someone is being arrested is Mirandization required. Although your boyfriend was questioned, he wasn't arrested and the police were not required to read him his rights. Miranda is really designed to protect citizens after they have been arrested.
You only need to be read your Miranda rights once you are arrested. You can be questioned without being arrested. If no charges had been filed, then he technically could have left the questioning whenever he liked, since he wasn't under arrest. The police did nothing wrong.
They don't need to read him his rights because he was not under arrest, he was just being questioned on the crime. If they were to arrest him they have to read him his Miranda rights.