[makeitdouble]

Setting aside my other response, a better way to look at it is that you declare your purpose on entry, but you're not the one judging if it's appropriate or not.

We/You can see remote work as not invalidating your claim, but that's just how we feel, not how it will be judged. To your larger point, the rules being mildly fuzzy aren't helping foreigners in general, it's usually more leeway for the authorities to pick and choose.