While this is correct, something important is neglected.
If P implies Q which implies R ... and if I find a problem in R, I have to check back to Q and P. Modus tollens.
Rational thinking is a whole belief network's re-examinator, when used properly.
You are emphasizing the truth-values at the nodes of the belief network ("check back to Q and P"). That is important. After all, in the end, you do want to have the right truth-values in the buckets.
But there are also structural questions about the underlying graph. Which edges should connect the nodes and, perhaps more deeply, which nodes should be there in the first place? When should new nodes be created? These are the questions addressed by Phil's and Anna's posts.
AnnaSalamon's recent post on "flinching" and "buckets" nicely complements PhilGoetz's 2009 post Reason as memetic immune disorder. (I'll be assuming that readers have read Anna's post, but not necessarily Phil's.) Using Anna's terminology, I take Phil to be talking about the dangers of merging buckets that started out as separate. Anna, on the other hand, is talking about how to deal with one bucket that should actually be several.
Phil argued (paraphrasing) that rationality can be dangerous because it leads to beliefs of the form "P implies Q". If you convince yourself of that implication, and you believe P, then you are compelled to believe Q. This is dangerous because your thinking about P might be infected by a bad meme. Now rationality has opened the way for this bad meme to infect your thinking about Q, too.
It's even worse if you reason yourself all the way to believing "P if and only if Q". Now any corruption in your thinking about either one of P and Q will corrupt your thinking about the other. In terms of buckets: If you put "Yes" in the P bucket, you must put "Yes" in the Q bucket, and vice versa. In other words, the P bucket and the Q bucket are now effectively one and the same.
In this sense, Phil was pointing out that rationality merges buckets. (More precisely, rationality creates dependencies among buckets. In the extreme case, buckets become effectively identical). This can be bad for the reasons that Anna gives. Phil argues that some people resist rationality because their "memetic immune system" realizes that rational thinking might merge buckets inappropriately. To avoid this danger, people often operate on the principle that it's suspect even to consider merging buckets from different domains (e.g., religious scripture and personal life).
This suggests a way in which Anna's post works at the meta-level, too.
Phil's argument is that people resist rationality because, in effect, they've identified the two buckets "Think rationally" and "Spread memetic infections". They fear that saying "Yes" to "Think rationally" forces them to say "Yes" to the dangers inherent to merged buckets.
But Anna gives techniques for "de-merging" buckets in general if it turns out that some buckets were inappropriately merged, or if one bucket should have been several in the first place.
In other words, Anna's post essentially de-merges the two particular buckets "Think rationally" and "Spread memetic infections". You can go ahead and use rational thinking, even though you will risk inappropriately merging buckets, because you now have techniques for de-merging those buckets if you need to.
In this way, Anna's post may diminish the "memetic immune system" obstacle to rational thinking that Phil observed.