I think this depends on the professor. Some would be delighted to know about your passion for the topic, as well as the 'additional research' you've done. Of course, there are those who don't like that you think on your own, because to them it might seem disrespectful (this surely depends both on the person's perception and your presentation itself).
It's definitely important to never make it personal (look like you want to show that you know better or that the professor himself/herself is wrong). Could information in a textbook (better if they didn't write it themselves) be wrong or outdated? Of course it could, and some will want to know. However, a test might not be the best place to make your impact.
You might be able to discuss the topic with your professor outside of a formal test, either by E-mail or otherwise. It should be okay that a student wants to contribute and help out, if that's how it ends up appearing.
If you want to go more in-depth in the oral exam, some will and others will not allow this. E.g. some, once they've heard enough about a single topic, will skip to the next one in order to save time, so there might not be time for you to provide additional information. But if you want to do so, just make it look like additional information, and not exactly a "this is all wrong, and this is correct" kind of thing. For that, you need to have more than your personal knowledge (scientific references, trusted sources, better yet sources that the professor considers reputable), and is better discussed outside of a test. I don't know if you have E-mail communication, but it might be one channel that allows you to provide links and references without imposing any pressure or seeming disrespectful (of course, that still depends on how the content is formed).
With some people, they will dislike you personally for trying to provide this information. This result is awful. You didn't help them, and you didn't help yourself either.
Other people are open to communication. With them, you may feel good for trying to help out and modernize the class/exam for future generations. In the end, you have to trust your feeling and anything you know about the specific person in this case.