I had to try and figure some of this out when adding fuel based route planning to
Auto-Jimmy. I've looked through the source books I have and have a theory.
The Mongoose 2e Traveller Companion clarifies some of this, but it also makes things less clear at the same time. In the section covering starports and spaceports (p125) it says that class A starports sell refined and unrefined fuel. Where it makes things less clear is that the description for class B starports makes no mention of fuel at all, however, the description for class C starports say unrefined _and_ refined fuel is usually available. That last part seems particularly unexpected as it's quite a big deviation from the 1e, 2e & 2022 core rules.
As others have pointed out, the CT rules may be relevant here. The oldest copy I have access to is from 1982. In it, the description of A/B starports (p84) just has "refined fuel available", but if you also factor in the wording for C/D class starports where it says "only unrefined fuel available", my interpretation would be that this implies unrefined fuel is available at A/B starports otherwise their descriptions would state "only refined fuel available". This seems to be further backed up by the fact the example adventure included in those rules says Alell Down Starport is class B and sells refined and unrefined fuel (p141).
It's also worth noting that the T5 core rules have clarified things further by explicitly stating that A/B star ports sell refined and unrefined fuel, whereas C/D only sell unrefined.
This is pure speculation, but my theory is that the Mongoose rules were always meant to be the same as CT where A/B starports sell refined and unrefined fuel with C/D only selling unrefined, however, a subtlety in the wording from the CT rules was lost when Mongoose updated the rules and switched to having this information in a table. An attempt was made to clarify this in the Traveller Companion, but a mistake was made, and refined fuel was added to the description for class C star ports rather than unrefined being added to class B starports. Like I say, it's pure speculation and there are a few leaps of logic, but (to me at least) it makes more sense than the Traveller Companion intentionally adding refined fuel to class C starports. It would be really intereasting to hear from someone at Mongoose if that was actually the intention.
In an actual Traveller universe, I expect there wouldn't be a hard and fast rule, but I would think the vast majority of A/B class starports would sell unrefined fuel if they could. As others have mentioned, the prevalence of ships with fuel refiners, risk/time involved in wilderness refuelling and the difference in cost between the two types of fuel would mean there would be a market for purchasing it in most systems. Even if the starport themselves didn't sell it, then some other entrepreneur in the system would fill the gap.
One exception to this might be systems where the main world has a lot of surface water, so wilderness refuelling is low effort _and_ low risk. At that point the demand for unrefined fuel might be lower, although I expect there would still be demand from ships that can't (or don't want to) go into atmosphere.
The other exception I could think of would be systems where wilderness refuelling isn't possible at all. At that point it's a seller's market, so a starport could get away with only selling the premium fuel. In that kind of situation, it might be harder for a smaller entrepreneur to fill the gap, as the cost of getting fuel shipped in may be prohibitively expensive. However, I'm not sure if a starport doing that would be in their own best interests. If every ship going there is forced to pay exorbitant fuel prices in order to leave the system, then a lot of them are just going to decide to not go there. This would seem counter productive from the starports point of view.