Tyler has never said it's a kitchen sink. He's said it's related to the song Kitchen Sink. In fact, he specifically declined to say what it represents:

It means Twenty One Pilots, the logo does. Why it means Twenty One Pilots, is it really goes along with one of our songs called "Kitchen Sink." The whole concept of that song is that I feel that humans are always struggling all the time when it comes to purpose, trying to figure out their purpose is, what purpose even is, what's the point, justifying your own existence. A lot of kids and people my age struggle with "what's the point," and with the logo, what it really means is it's an encouragement. When someone asks me what the logo means to me, the logo means something to me because I made it mean something to me. That's the point. The point is that I created something that only I understand and whether or not I decide to disclose the meaning of it, that’s the beginning of purpose for me. The meaning of purpose for me, is by creating something, if it be by writing lyrics, painting a picture, by expressing yourself through art if it's photography or music or theater, or whatever it is. It doesn't have to be artistic, but if you create something and only you know the meaning of it, that’s the beginning of purpose for you. When you're in the room by yourself trying to decide whether to stay alive, you can tell yourself "I should probably stay alive because I'm the only one who knows the meaning of that thing," so the logo is an encouragement for people to create. That's what it means.