halacha - Does extra virgin organic coconut oil have to have a hechsher?

I am specifically referring to Coconut Oil. I know that my question is similar to this one: Is Extra virgin olive oil kosher by default? but My question is also about non-olive oils. Due to the huge olive oil industry there is a large profit to be made in manufacturing fraudulent products which is part of the analysis as to whether or not to permit (extra virgin) olive oil without a hechsher. In addition the product I have says: Free of: Milk, eggs, peanuts, shellfish, fish, soy, gluten, titanium dioxide. The specific product I am referring to can be seen here: http://www.vitacost.com/vitacost-extra-virgin-certified-organic-coconut-oil-54-fl-oz-10