I don't know much about stats, but does "the null is that the success rate is the same" imply that it's a sketchy methodology because they can come up with some findings ("ruder prompts are better/worse!") more often?

You are asking about one-sided vs two-sided tests. Not really "more often" because formal type 1 error rate is still the same. I'd say two-sided tests leave more space for post-hoc theorizing but there are valid situations when there is no clear one-sided hypothesis a priori. Do we really know whether that the hypothesis should have been "ruder prompts are better"?

I'd say this is benign compared to other ways of (mis)using statistics e.g. looking which way the difference goes and then running one-sided tests or tweaking the setup until one gets "significant" p vals.

EDIT: I looked in the paper again and noticed that they actually did pairwise t-test on all possible combinations of tones. They should have adjusted for multiple testing since they are doing 10 tests (choose 2 from 10) and not one.

That's the usual null hypothesis for these kinds of tests.