In the scenario where you are about to depart from a non-tower aerodrome which has no weather reporting and lies inside someone else's CTR, I imagine it's up to you to assess the weather conditions to the best of your abilities and make a decision as to whether you are legal to go or not and under which conditions (and of course, whether it's a good idea at all). E.g., if your aerodrome looks like in VFR conditions, then you may depart as usual, but if you're then transiting close to a controlled airfield where the METAR shows viz requiring SVFR, then you must request SVFR for the transit. That's just my interpretation anyway--I could very well be wrong, but I don't think the rules go to that level of detail.
In practise, nobody will care unless you have a prang, but try to be sensible.