Based on the specification of ResourceBundle.Control.newBundle in jdk 11, the method will throw IllegalAccessException if the class or its nullary constructor is not accessible. But the IllegalAccessException is not thrown.
I checked the source code, since jdk 9, ResourceBundle.Control.newBundle is changed, if constructor of the resource bundle is not public, it does not throw IllegalAccessException, only when unnamed module loads a resource bundle in a named module which are not open, the exception will be thrown.
JDK 12:
3178 // To access a resource bundle in a named module,
3179 // either class-based or properties-based, the resource
3180 // bundle must be opened unconditionally,
3181 // same rule as accessing a resource file.
3182 if (m.isNamed() && !m.isOpen(bundleClass.getPackageName())) {
3183 throw new IllegalAccessException("unnamed module can't load " +
3184 bundleClass.getName() + " in " + m.toString());
3185 }
3186 try {
3187 // bundle in a unnamed module
3188 Constructor<ResourceBundle> ctor = bundleClass.getConstructor();
3189 if (!Modifier.isPublic(ctor.getModifiers())) {
3190 return null;
3191 }
3192
3193 // java.base may not be able to read the bundleClass's module.
3194 PrivilegedAction<Void> pa1 = () -> { ctor.setAccessible(true); return null; };
3195 AccessController.doPrivileged(pa1);
3196 bundle = ctor.newInstance((Object[]) null);

Run attached sample code:
8u191 build 12: passed
12 build 20: failed
11.02 build 04: failed
Error log:
Exception in thread "main" java.lang.RuntimeException: getBundle("PrivateConstructorRB") throws null, expected class java.lang.IllegalAccessException
        at MissingResourceCauseTest.callGetBundle(MissingResourceCauseTest.java:18)
        at MissingResourceCauseTest.main(MissingResourceCauseTest.java:5)