My olive oil didn't solidify in the fridge. Is it fake?
How liquid was it when you say liquid? Our kitchen is very cold in winter and may very well get to fridge temperature at night time and the olive oil gets white balls of solidified oil in it, and then goes very sludgy, making it difficult to pour, if not impossible. But it doesn't exactly solidify. So it depends on whether you mean it is completely liquid like normal or not. 

This website implies that most oils should be unpourable by 35F (1.7C), which is the lowest temperature for a fridge (i.e. any particular fridge or part of a fridge may be slightly warmer than this):
http://www.oliveoilsource.com/page/freezing-olive-oil
(This same information is found on a multitude of sites, so I do not believe this is the original source)

However, it also says that olive oils may be "winterized" which means they do not clump or cloud, even at 32F/0C. This is so they can be used in salad dressings, etc, that are stored in the fridge. So you would need to find out if your olive oil had been so treated. I am not sure if this process is just used for oil sold for commercial use or not.