What is a fair review?

I've recently had a very mild case of being trolled when someone moaned about a review I wrote of a book called Chilled. Before anyone thinks I got too horrible in my opinion, I ought to point out that I gave the book four stars, was very positive about it and the publisher gave every evidence of being highly pleased with the review. But someone wasn't, as I received this tweet:

If this sounds rather confusing, I had said in my review:
There are comments on both the front and back covers by Tony Hawks. Now, my first inclination was to wonder what a pro skateboarder had to do with the science of cooling. But it turns out that this is Tony Hawks the comedian and raconteur. Ah, well, it's obvious what his connection is. Well, no, it isn't. Apparently he did a TV show and/or book where he went round Ireland with a fridge, and this is the only reason for having him along to give the book a puff. It seems, to say the least, a little tenuous.
A review, recently
(Incidentally, I know the pro skateboarder is Tony Hawk, not Tony Hawks, but in my defence, I once briefly reviewed computer games for a living, and one was called Tony Hawk's Pro Skater or some such, so I've always considered it fair game to appear to get them confused. I thought it was, to quote, 'rather a good joke', and I was sorry it wasn't for my critic.)

I thought I'd explain a bit more. And we got into a 'discussion' about whether or not you have the right to say what you want on a review site.

The final riposte from my critic was that the freedom of the internet also allowed him to comment on 'unfair criticism like this.' And this is what got me thinking about what makes for a fair review. Was what I had written unfair criticism? Really?

If I had said something about the book that wasn't true, yes, it would have been unfair. But I honestly don't think the review was unfair - nor was there anything non-factual about my comment (okay, apart from the joke about Tony Hawk).

In the end it comes back to the reality that reviewing is a subjective art - it is a published opinion, not a scientific measurable fact. The review, including the (brief) moan about the puff on the jacket was my opinion. If someone doesn't like it, that's fine. Perhaps they should set up their own review site. But there really is no point arguing with a review simply because someone else doesn't like something you do.