Of course they are, it's not like Amazon really cares much. With all the power of AWS and deep learning etc., identifying fake reviews should be a piece of cake if you are Amazon. It doesn't affect the bottom line, so why bother.
I guess I feel more comfortable commenting on this vs such posts about Google (my employer) because I don't have to worry about leaking anything important but this is absolutely not a piece of cake. Anyone who has worked on planet scale anti-abuse systems knows this is a very tough and never ending problem. You think there are obvious signals for good or bad - the 0.01% cases where this does not hold up turns to 20 m…
But if you look at e.g. seller forums at Amazon, there are a lot of large threads about the opposite problem - Amazon taking out lots of reviews the sellers consider legitimate.
So clearly they are doing something, and it might even be that only a small minority of fake reviews get through, but due to Amazon's scale there are still a lot of them.