>Cement/Concrete (based on Portland cement) is water proof

That's patently untrue. Otherwise we wouldn't need concrete sealants.

You can also just see it with cement board - if you pour water on top of it, it will eventually migrate through and drip.

You are correct.

I'm not sure why I remember cement to be water proof. Its possible I infered from how its been used around me. I have seen cement very often used where water contact is expected (bathrooms etc). I have also seen brick walls plastered with an extra layer of cement as putty considered to be rain proof and any leaks were thought of as poor workmanship rather than poor material choice.

P.S. I'm not a builder. I've taken an interest in the topic a few months ago.

The key here is “based on Portland cement”, which is generally has water repellent added to it making it water proof.

Normal cement, concrete .. Is a different story.