Yeah; I'm pretty sure that isn't the case. They don't care if you do work online while visiting, just that you're not looking to stay or to take a local job (that they'd prefer to go to a resident). The legal language may be a little fuzzy since I bet it was written before remote work (telecommuting if it even existed at the time :P) was as much a thing, but I'd challenge anyone to find a case of someone penalized for working for doing their job remotely from another country.

That said, if you're working for a multinational company, you may want to be careful. Being hired in country A, for a company that has presence in both A and B, and then flying and working for a few months in B, could conceivably raise all sorts of flags if noticed.