Short version: I doubt that resupply ship had any fuel in its cargo.
I assume your fleet is not something crazy. Like 40 cruisers, or something similarly giant. Fuel can be one of the fun challenges of this game...
Large spaceports are a good spot to refuel. If not, you got a local fuel shortage. Multiple large fleets hitting the same spaceport is likely to run it dry even if it has lots of nearby gas mines.
I have a habit of always booking a fuel mine when I get a new colony. Select the source, and click the "gas mine here" button below the selection panel (as long as you have enough expansions for those buttons to appear).
The resupply ship thing sounds odd. It has to be deployed on a fuel source, and it has to have the same fuel that your fleet uses. Or, reputedly, it does not have to be at a fuel source, but it needs one to fill its cargo with fuel. If empty, it also needs some time to mine fuel. By double clicking the selection window with the resupply ship selected, you open it in the ship list. Do this and inspect its cargo. For anyone to refuel, it needs unreserved fuel in cargo.
It sounds like for some reason there was no fuel on your resupply ship.
A trap in fuel management is mixed fuel in a fleet. You have a nice alien cruiser on a hydrogen reactor in a fleet of your caslon powered ships. This fleet becomes a pain to refuel (it needs both types). If the resupply ship is on a pure caslon source, the fleet will not want to go there (but you should be able to tell it to do that).
A resupply ship should manage to refuel two fleets, but there is a feature that may have the AI send the second one somewhere else. The first fleet with refuel order will reserve enough fuel to fill its fuel tanks from empty to full, even if it has half fuel. If the second fleet gets refuel order (at nearest), the first fleet may have reserved too much for it to consider the resupply ship. You may know, though, that there will be enough fuel for both (the ship should mine more too). In this case manually right-clicking the resupply ship with the fleet selected allows you to order it to refuel at that specific ship (even if it is short of fuel). This could give the "standing outside" behavior you observed if there is no fuel to be had.
That way of specific ordering is useful also for repairing/retrofitting at the right spaceport, refueling at the correct spot, loading/unloading troops at the correct colony, attacking the correct target... Often I do not want things to be done at "nearest", I have specific ideas about where to go.