We s̶h̶o̶u̶l̶d̶ want to successfully correct people when they use wrong methods to arrive at an answer, regardless of whether the answer is correct or not.
['should' replaced with 'want to successfully' in response to comment below by Shokwave.]
In the post that you linked to, Eliezer wrote:
I try to avoid criticizing people when they are right. If they genuinely deserve criticism, I will not need to wait long for an occasion where they are wrong.
It seems to me that Eliezer avoids criticizing people when they are right because it takes more effort to convince them that their methods are incorrect in this case. In other words, the (social, cognitive, etc.) costs of correcting someone's reasoning are greater when their final answer is correct.
I found JoshuaZ's comment to be uninformative because he did not provide evidence for his implicit claim that Cowell's beliefs about cryonics are from faulty reasoning (or other traits associated with stupidity).
We should correct people when they use wrong methods to arrive at an answer, regardless of whether the answer is correct or not.
The goal is not to emit truthful propositions; the goal is to make the other believe truthful propositions. Paraphrased from Pavitra's comment.
Avoid criticizing people when they are right not because it takes more effort to convince them - but because all your effort will merely convince them more strongly of their own position, thanks to hardwired faults in the human brain.
From a GQ interview: