Can Spring init Bean(Factory)PostProcessor lazily?

Could anybody explain me it? After reading the documentation I didn't understand.

Can Spring init Bean(Factory)PostProcessor lazily or not?

https://docs.spring.io/spring/docs/current/spring-framework-reference/core.html#beans-factory-extension-factory-postprocessors

There is a such block that confuse me:

As with BeanPostProcessors , you typically do not want to configure BeanFactoryPostProcessors for lazy initialization. If no other bean references a Bean(Factory)PostProcessor, that post-processor will not get instantiated at all. Thus, marking it for lazy initialization will be ignored, and the Bean(Factory)PostProcessor will be instantiated eagerly even if you set the default-lazy-init attribute to true on the declaration of your element.

The correct answer to the question: "Can Spring init Bean(Factory)PostProcessor lazily?" is "NO". I checked it by myself. I created 2 classes:

@Lazy
@Component
public class CustomBeanFactoryPostProcessor implements BeanFactoryPostProcessor {
    @Override
    public void postProcessBeanFactory(ConfigurableListableBeanFactory beanFactory) throws BeansException {
        System.out.println("bean factory!");
    }
}

and

@Lazy
@Component
public class CustomBeanPostProcessor implements BeanPostProcessor {
    @Override
    public Object postProcessBeforeInitialization(Object bean, String beanName) throws BeansException {
        System.out.println("before init!");
        return bean;
    }

    @Override
    public Object postProcessAfterInitialization(Object bean, String beanName) throws BeansException {
        return bean;
    }
}

And run spring application. So, in console it was printed: "bean factory" and several times "before init", although I put @Lazy annotation on these classes.