Personally, I disregarded the story once it claimed that Turing being outwardly happy was evidence he was not suicidal. I thought it was well-known that someone may be suicidal and hide it from everyone. Once I realized the author didn't understand that, I had no trust in everything else he said.
Anyway, that's a good explanation of a phenomenon I have observed as well.
There's a certain mindset that delights in anything that goes against conventional wisdom. Sometimes this is really useful, but the thing is that conventional wisdom is actually right most of the time. A knee-jerk reaction to believe anything that goes against conventional wisdom is no better than a knee-jerk reaction to disbelieve it. A lot of people have this tendency, even very smart people. I'm sure I fall victim to it myself sometimes.
The "Turing didn't really commit suicide" article was perfect for that. It takes a classic story that's attained the status of modern (albeit relatively obscure) myth and turns it on its head. It's attractive for the same reason that articles about radiation being good for you, peak oil being a myth, and the civil rights movement being bad for minorities are attractive: they're intriguing ideas that make you feel smarter than the average joe, since they contradict what "everybody knows".
It's often pretty easy to pull off, too, because most people don't do much research into the things "everybody knows". "Everybody knows" Turing committed suicide by eating a poisoned apple. But few people know the details. Thus, when an article says that the apple was never tested for cyanide, it's extremely convincing, because few people are aware that it was found in Turing's stomach. Likewise, the article discusses Turing's cheerful mood in his last days as evidence against suicide, even though it's actually at best neutral if not evidence for suicide. But most people don't know that elevated mood prior to suicide is common, and not having researched the "everybody knows" story, they'll take it as evidence of the alternative theory.
It's an interesting phenomenon. People will go their whole lives knowing the official story but not knowing any details. Then one single article comes out with a few details and suddenly they're convinced that what they knew their whole lives was wrong, even without doing any further research on their own. I must admit that I went through this exact process with this story, reverting to a sort of generic detail-free skepticism a little while after reading the Turing-didn't-commit-suicide story, and only realizing how silly it was after reading jgrahamc's comment here.