So I just tested that and no, interestingly enough, that is not the case. As soon as a city has grown onto a tile that tile gets "owned" by that city, which then means that, after all, I was right - just in the wrong way.
So my conclusion is: Resource tiles are still "owned" and assigned the second the tile gets dragged into your borders just as I thought, but if multiple cities can own a tile, then, no matter which city you use to buy that tile, the game will always give that tile to the same city - I tested that ingame:
I bought a resource tile that was in the third ring of my capital, just after I finished a city that then had the resource tile in its second ring, and as expected, although I actually bought the tile with my capital the other city is the one that is allowed to construct the resource building.
Out of interest I then did some more tests: Selling the building in the capital did, as expected, not change anything about the ownership of the resource. But when I deleted my capital, the other city got the right to construct the resource building. So tiles get re-distributed when the original owner vanishes. However, as already mentioned, founding a new city closer to that resource after it has already been claimed does nothing. With the exception that, after some more digging I finally managed to break that system:
As one can see there's only one tile of petroleum in the radius of that city and it has been claimed (bought) by Citadella (it has also already built the Petro-Plant), before the outpost grew onto that tile. The city now shows that the petrochemical plant could be built if a Petroleum-Tile in its proximity got improved, but the only Petroleum tile that is available has already been improved and belonged to the capital. The moment I remove the resource from that tile the Petrochemical Plant is no longer listed in the building menu.
I actually had to think about that for a while, but if it's not just a bug that was caused by me using IGEditor out of laziness, then I think here's what happened: That resource DID change ownership when the city was done, so it seems the "The resources around a city always belong to that city"-Rule is correct. The problem is that that tile was improved before the ownership was changed so the new city thinks it's not improved. And the only way to fix that is to let an AI plunder that tile and then repair it - at that moment you can build a second Petro-Plant from the same Petroleum-Tile. Not sure if that's really worth it though.
