It's mostly true but not all of it. China did reclaim the Spratlys and Japan renounced their own claims to them after WW2 but also France has a claim on the islands that it has never officially renounced. The difference is that China has also continuously occupied the islands since then and the French attempted to but failed. The USA also warned the Philippines in the 50s not press their claims on the islands as it's owned by China. This is just to establish that China has a legitimate claim that is internationally recognized but are not the only country that intended to occupy it. There are a few other countries that also have claims to the area which I didn't list. The point is even if there wasn't oil in the area there would still be a territorial dispute but oil without a doubt contributes to this dispute.

edited for source: The De-escalation of the Spratly Dispute in Sino-Southeast Asian Relations by Ralph Emmers and also: The Spratly Islands dispute: who's on first? by Daniel Duzrek