I just tested this out a little bit, here’s what I found:
It is definitely showing larger airfields in the zoomed-out views, to get the smaller ones you have to zoom waaaay in (entering them in the search bar works, too). Here’s a trio of airfields in southeastern Wyoming - KSAA is Saratoga, an airfield with an AWOS and METAR, WY11 is a private airport at a ranch with a long paved runway, and 96WY is a private strip with short turf runways. Note that 96WY doesn’t really show up until you zoom in, but it’s there.
Here’s the current METAR at KSAA as displayed in the flight planner (also pointing out that the current isogonic line in that area is 9°E, but the value used in the planner could be from an older survey):
Clicking on “more details” we get this, which matches the METAR:
However, if we do the same at WY11, which doesn’t have a METAR, but is only 22nm away from KSAA at a slightly higher elevation, we get this:
Note the discrepancies in temp, wind, and altimeter. I highly doubt it’s off by that much. Now, I’m not at a computer and can’t test whether these are the conditions currently portrayed in the sim, but I encourage anybody to do so, comparing against the latest weather in flight planner when you do so, of course.
Further, this is what aviationweather.gov is putting out there for current temp and wind forecasts in that area. Note the surface temp is roughly the same, and the winds are gusty out of the south.
And for the sake of comparison from ForeFlight, here’s the hourly weather forecast at WY11:
Definitely not 14°C (57°F), nor 1 knot winds. I’m willing to bet the sim will have stronger winds, but again I can’t test right now.
In the end, this jives with your conclusion that the non-METAR airports aren’t displaying the right weather in the flight planner - they’re displaying something, but I’m curious to know whether the sim is doing the same and if so, where is it getting that info for the spaces in between reporting stations. More testing needed! 
Thanks so much for your input, very appreciated!