I cannot say personally that either analysis is wrong/right. Vegetable, in the sense of "coming from a vegetable " exists as an adjective
http://www.merriam-webster.com/dictionary/vegetable. It can also IMO be taken as a noun used adjectivally as is said in one of the agrees. Anyway, this is what is usually taught to English learners, when several adjectives qualify a noun.The adjective which is the most permanent characteristic of the noun goes closest to the noun. (e.g. she is a beautiful English woman - she will always be English, she may not always be beautiful). Vegetable is more characteristic (here) of this particular oil (ie it's not olive oil) than pure (there may be vegetable oils which are less pure).
We can also say that it is a compound noun designating a category of oil - olive oil, sunflower oil, grape-seed oil or whatever. I would say both explanations in the case of 'vegetable'(adjective/compound noun) are totally justifiable...
Of course, looking at 'sunflower oil, grape-seed oil', one might choose compound noun, ( similarity of construction) but I am not convinced we can say categorically that vegetable oil is one or the other.. (+ does it matter?!)