The general definition of an insurance binder is a temporary insurance contract that provides proof of coverage until you receive a permanent car insurance policy. However, the definition and point of actual coverage is different for every state and also different for each policy.
Typically an insurance binder is immediate insurance coverage that can be in oral or written form. The binder's purpose is to provide temporary insurance coverage for a specified time until a formal policy is accepted or denied.
Most policy language sets policies effective the next day at 12:01 AM, so some agents do not have the authority to issue a binder that is effective immediately. A binder is issued by an agent to the customer, so your boyfriend should contact his agent to determine why they state he is not covered and when the binder would have been in effect for coverage if it was not at the time of the accident.
If he needs more information on understanding auto insurance binders he can contact you state's Department of Insurance for consumer help.