I've never heard the phrase but I think you're partly right. I don't think the nine letters all had the same content though. I think probably it was clear from each individual letter that it was simply an impersonal response, a letter which was printed over and over again and simply sent out to lots of different people.
In BrE, we call them "stock letters" or "stock responses". You formulate a rather bland response to a commonly asked question or request and whenever such a request is received you can just add "Dear Mr XXX" at the top of the standardised letter and send it out. It requires no thought or effort.
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