REF_invokeInterface resolution is not specified to perform check of ACC_PRIVATE flag of the resolved method.
HotSpot throws IllegalAccessError if the resolved method has ACC_PRIVATE set.

Example:
public interface InvokeInterfacePrivate version 52:0 {
     public static Method main:"([Ljava/lang/String;)V" stack 10 locals 1 {
         ldc MethodHandle
REF_invokeInterface:InvokeInterfacePrivate.m:"()V"; // throws
IllegalAccessError
         return;
     }
     private Method m:"()V" stack 0 locals 1 { return; }
}

This is akin to the assertion jvms-6.5.invokeinterface.linking-110 in invokeinterface spec: "Otherwise, if the resolved method is static or private, the invokeinterface instruction throws an IncompatibleClassChangeError." (Part related to static methods is discussed in JDK-8138569)