Apple's policy is completely consistent here. If you are a browser then you don't control the data that the user is accessing. But with all other apps especially Tumblr you do control the data.
That was my take, too. While it's certainly true that Apple can be inconsistent and even weirdly capricious, this wouldn't be the first time a company has preemptively "censored" themselves on the App Store.
While it's true that a Tumblr app is a bit different from, say, a web browser, it's not really true that Tumblr has a high level of control over the content on their own service -- no more than a service like Twitter or even Facebook does.
