The current SDK only allows 3rd party apps to access the watch through "glances" (notifications), but there are a few third party apps with exceptions. The reason is not that the watch cannot store apps on the watch, but that Apple wants to tightly control how much access developers have to the watch in the beginning.
Apple has said third party apps running natively on the watch are going to come later, possibly June with WWDC? So, while third party apps don't work without a phone now, thats not going to be true for long.