If you're going to respond empathetically to someone who you think needs help, it's important to distinguish that from a personal attack. This comment doesn't do that—indeed it almost seems like you're invoking "psychiatric help" as ammunition in an argument, which would be bannable offence here.
It's almost a moot point. Given the underlying pathology, any attempt at all to discredit this type of delusion* will necessarily be seen as a part of the conspiracy, and hence as an attack. No amount of empathy will help.
But I certainly see what you mean; I was probably too quick to use that stock phrase. My intent here wasn't to argue, because I know that's impossible; it was more to identify the pathology to others. Would my comment have been fine without the last line? (I'm assuming that you were the one to flag it.)
*: and I mean that in the psychiatric sense, not as an insult
I think you'd need both to drop the last line and reword the first line, because otherwise it's too easy to read as invoking a psychiatric category as snark.
There's probably a way of making this point that's fine, but it would require pre-emptively distinguishing your comment from the obvious misinterpretations. Which is tedious, but such is the way communication on a large forum needs to work, or else people just react and attack.