Yes, you assume DM fiat is not being used to block the build on a whim. But just because the rule points out that a DM may allow a weapon not on the list, it doesn't mean you should assume the DM will allow it. The DMG effectively states that a DM may allow anyone to do anything at any time. That doesn't mean you should base a build around that.
Since the text "little thrown weapon" is a "barely qualified statement of relative size", which doesn't include any real in-game guidelines (size category, weight), and the author included a list of weapons, I don't see any reason not to stick with that list. As I said before, if the author intended the ability to be used with any thrown weapon weighing 1 pound or less, they easily could have just said that. But they didn't.