Is cooking oil a safe preservative for vegetables?

Not entirely. It excludes air, preventing moulds and oxidisation, but unfortunately oil doesn’t stop the growth of anaerobic (ie not dependent on air) bacteria — and one of these is Clostridium botulinum, which can lead to fatal results. It’s rare in New Zealand, but to avoid any chance of botulism in vegetables preserved in oil either keep them refrigerated and use within a week or so, or briefly cook in vinegar before covering with oil (fruit is okay because of its acid content).