http://edition.cnn.com/2017/01/24/foodanddrink/millenary-olive-trees-spain/index.html
I checked Ulldecona up on Google map to make sure the sentense in the article.
"Although it's possible to reach Ulldecona by train, we recommend traveling by car."
It's located between Valencia and Barcelona, and it's more than 150km to each city.
The condition has been good to preserve old olive trees. That's because it avoided exploitation as suburb of both cities, but for vegetable, it's a good distance from huge consumtion area.
As well as those conditions, Mediterranian Sea Climate must have helped the growth of olive trees.