Actually after having a quick lil Google about this, companies that mention "political activity" in their guidelines are in the minority (1/4) and Basecamp may

Actually after having a quick lil Google about this, companies that mention "political activity" in their guidelines are in the minority (1/4) and Basecamp may actually be contravening the NRLB guidance on political speech - particularly since its pretty clear that the political speech in question was surrounding a matter at the workplace. So no, they don't "absolutely get to define what the company handbook means" - there are legal boundaries to what they can prohibit. Additionally, we should be absolutely cynical about companies prohibiting political speech. As this Basecamp example shows, they'll attempt to do so about workplace matters.