Exactly, Mirth.
Any small progress that is being made here has nothing to do with Trump or the US, really. If anything it happens in spite of them like usual. This instance to always read the world with American glasses is hilarious. The mess on the Korean peninsula is American-made, that much is true, but that's rarely the angle people focus on. Let's keep giving them credit for any diplomatic relationships that have been established and keep talking down to the Koreans.
South Korea have softened up Kim for years now while the Trump administration has done nothing but trying to agitate a nuclear war. North Korea were invited to the winter olympics while Mike Pence showed up with Otto Warmbier's father as his +1. The meetings between Moon and Kim happened without American interference - which is probably why they happened at all.