I've been told that it requires you to relax in the water and trust the water to support you.

Most people that have difficulty floating from what I have seen are either very, very dense, like low body fat individuals with high muscle, or they stay tense in the water, and so they can't actually relax and allow the water to float them.

I think, from what I understand, that that does not qualify as swimming, in that case. I am not a swimologist however, so take my words with a grain of salt.