When did I say close cousins? I specifically said distantly related. Whether they are distantly related or not, they share DNA. Are you denying this fact? I don't believe the Uzumaki are direct descendants of Ashura, but I do believe Uzumaki do share some heritage with Senju, meaning they share DNA and thus are related, distantly of course.
Its time to squash the bug. Distantly related and direct descendants are two completely different animals. You likely don't get this because direct bloodlines [descendants] don't really exist in the real world. Direct bloodline basically means you are the offspring of 2 parents that are part of the same lineage. This would be likened to both your father and mother being related, like cousins for instance. Obviously mankind has learned over time that marrying your cousin can cause mutations in your DNA, and this is why these practices don't regularly exist.
In the world of Naruto, clans are of the same bloodline. This means that all adults in the Uchiha clan were some form of cousin, be it distant or not, so they were all directly related. Considering the fact that Uzumaki and Senju do not share a clan name, that means they are not directly related. What it means is that the Uzumaki clan was an offshoot of a Senju marrying outside the clan.
Its like this, a Senju marries outside the clan and has children. These children also marry outside the clan, beginning to separate their own heritage from the Senju. Over time, this new family unit breaks off but then grows large enough that their immediate relations begin interbreeding. At that point they have created their own clan. That clan was the Uzumaki. At this point, they are related to the Senju but are not 100% Senju. Neither are they directly descended from Ashura, while the Senju are.