The BFS (spaceship, i.e. second stage) is supposedly going to have enough performance to make orbit on its own as an SSTO, with a tiny payload. It probably won’t ever be used that way, though.
You need supplies to keep those humans alive for a week, and a huge amount of fuel to boost the ship into a moon-intersecting orbit. Not a tiny payload by any means.
To get other BFSes up there with enough fuel to transfer a useful amount would require them to use the first stage booster instead of just being SSTO.
Really there's no point to doing an SSTO launch in practice since the BFR first stage will in theory be just as reusable (if not more so) than the BFS second stage. Using the first stage booster greatly improves payload to orbit and has relatively low marginal cost once you've built and tested the whole system.
For a single launch, sure.
What happens if there are regular launches?
Logistically, to me it seems that it would be a great idea to have a refueling station in orbit which is supplied by BFR cargo ships ..say.. once a month.
Launching a BFR for each launch of BFS would require a lot of transportation and duplicated effort.
Is this intuition wrong?
The plan is that the BFR lands back at the launch pad in the same cradle it launched from which would reduce operational complexity.
The fuel for your station has to get there somehow, and so does the station itself. The BFS-tanker ships would need to be launched with a BFR booster to bring up a meaningful amount of fuel, and there are going to be way more of those than there will be BFS-crew launches (ignoring the Earth-to-Earth transportation segment, where a centralized fuel station wouldn't make sense since each route will take a very different orbital path).
SSTO-ing the BFS-crew would require another BFR booster-plus-cargo launch anyway to replace the fuel and cargo you could have carried up in the BFS if you had launched it on the BFR booster to begin with.
The only angle that makes sense to me for doing a BFS-crew SSTO with minimal payload would be if it is deemed to be less risky for loss-of-crew. In that case you could have a BFS-tanker already on orbit and fully loaded by multiple BFR-plus-tanker launches, ready to rendevous with the BFS-crew ship after it reaches orbit on fumes.
I think that is unlikely though since such a launch might leave the BFS-crew without the fuel margin required to divert or de-orbit and land propulsively without refuelling.
Once your payload exceeds the SSTO capability of a single BFS launch, you save effort by doing a two-stage launch. The two-stage launch is more complex and difficult, but the added capacity is far greater.
For intuition, consider moving to a new house. What’s better, renting a tiny car with room for one suitcase, or renting a big truck? The car is cheaper and easier to drive, but unless all of your stuff fits in one suitcase, the truck is going to be much cheaper and easier for this task.
There is already a plan for a tanker version of the BFS, since as you note it wouldn’t be efficient to refuel with another crewed craft. I don’t see what the station helps with, though. That’s just extra mass to launch.
Managing logistics?
A series of BFR launches to station some fuel in orbit seems like a better choice than having to launch a fuel tanker BFR each time.
Why? I don’t see the advantage. It would make sense if one BFR tanker could launch enough fuel for multiple missions, which you’d then want to store somewhere, but that’s not the case.
Orbit isn't just one thing. The plane changes (some of the most expensive types of burns) involved to get to the same orbit as a tanker and then to the target orbit would vastly outway any potential benefits.
