It's not just small, private airports. The two, paved fields with no fuel on that map (KMCD and 5Y1) are both 3,500ft+ runways, with more than a few planes based at them. KMCD is even a major resort (Mackinac Island) with large twins and even an occasional twin-turbine landing there. Pumping fuel is a major investment with major resposibilities, and if the airport isn't busy, it's not economically feasible (in the case of KMCD it's that it's not only an island, but an Island that doesn't even allow motorized vehicles (except for airplanes, a fire truck and an ambulance (and a snow plow or two that come out of hiding in the off-season)).
So yes.. if you're based at a non-pumpimg airport; you either stop for fuel near home at the end of a flight... or plan on stopping not for from home when starting a flight.
I've yet to see a fuel delivery service for airports that do not pump, but I'm sure a few exist.
When I'm planning a flight through unfamiliar territory for real; I'll call all the potential fuel stops to confirm that they still pump and when they're open. Once, while flying through upper Michigan, I had to continue on to an alternate airport, pushing my VFR reserve, because the place where I stopped (and had called ahead) looked like I was the first person to risk pumping their fuel into a plane in years.. lol.
Even busy airports have their risks... If the 100LL and JetA pumps are next to each other, it's not unheard of for a busy, distracted lineman to pump kerosene into your C172
