I think that was her purpose of using oil, prevent oxygen absorption and thereby the spoilage. However it seems like the oil would turn rancid. As the other poster noted, storing fragile eggs seems risky.
The fragileness isn't as risky as you might think. I've used regular store bought eggs to make Easter pysanky eggs and they've lasted for years. Whole eggs with the insides still in them. Of course, the difference between my dyed eggs and the lady's eggs covered with oil is that hers are meant not to dry out so if they rot then gases may make hers explode.