Is it accepted/common to answer factually inaccurate reviewer comments in case of rejection?
I have not read your paper and it's likely that you don't work or publish in my field, so you will need to take this advice as it is given: without conditions or obligations.
I have decades of experience helping edit some of the top journals in my field. If I've learned anything, it's this: as much as academics like to think otherwise, peer-reviewed publications operate in much the same way as [insert trashy supermarket checkout rag here]. Journals are human institutions operated by humans with the same human concerns as everyone else. Things would go a lot smoother if they stopped being placed on pedestals.
Despite everyone's best efforts, mistakes happen all the time. From an editorial point of view, it is important to us to receive reports of factual errors so that we can consider the best information to reach the most appropriate decisions.
If you were to write to us about this issue, I promise you that we would consider this seriously. While we value the work our reviewers do, we also need to know when our reviewers are making factual errors such as this. This is actually a red flag for us.
- Why did the reviewer fail to pick up that these statements were referenced in the text?
- What else did the reviewer misinterpret?
- Is this behaviour consistent with other rejoinders or complaints we've received?
- Is it still worth our while keeping this person on our list of reviewers?
It is for this reason that I recommend that you compose and send a letter to the Journal making these corrections. It is unlikely that the issues you outline will overturn the decision and, by your own admission, you're not seeking an appeal. Nevertheless, I believe that this is an important step. There's no need to be uppity about this. Just lay out the issue and sign off.
In addition, you might want to reconsider the manuscript to see whether it could be improved to prevent this issue from being raised when you submit your work elsewhere. For example, you might have wrote
We collected and analysed blood using standard techniques. Levels of serum bicarbonate...
when something like this might be more specific
Analysis of serum bicarbonate was conducted using the process outlined by Nikishima et al. [5].
I'm making this up, but you get the idea. Could your statement be modified slightly so that there is absolutely no way for a reviewer to raise the original concern?
Anyway, good luck to you.
What you are suggesting sounds like a very honorable course of action to me. You are simply offering the editor feedback on the quality of service you (and the journal) received from the referee, which they can decide to pay attention to or ignore, at their discretion. Unless your field has some very strange norms of behavior/etiquette that differ markedly than mine (math), I see this as completely acceptable, and, while not exactly common, certainly not unheard of.
The only other advice I would offer is to take care that your feedback to the editor is offered in a professional manner, namely:
Be polite and respectful, and as concise as possible.
Make sure to mention that you are not asking for a re-evaluation of the paper at this time, due to the flaws you see in it yourself that are unrelated to your criticism and that you would like to work on correcting.
Explain that you are offering the feedback in the hope that it may be useful but are not asking for or expecting any action to be taken. When emailing busy people in such cases, I often include in the subject line the parenthetical phrase "(no action necessary)" or "(no reply necessary)".
Finally, make sure that the criticism you are offering is factually sound.
By the way, my answer that rebutting part of the referee's comments is acceptable would not be different if you were in fact interested in having the paper re-evaluated, though of course items 2 and 3 in the list above would then need to be modified accordingly.
Given that you are not expecting any change in the resulting rejection, and that this kind of inaccuracy happens all the time, it would seem inappropriate to contact the editor about this. Even though slightly annoying, it is very normal (at least in some subfields of CS) that some reviewers miss a few details (and, yes, sometimes, a single reference is a detail) and have to be more or less directly corrected in a response to reviewers.
If you still write any response to the reviewers, a simple statement in the answer to the reviewers such as
The claim X is based upon reference #.
should suffice. Leave it to the reviewers to figure that the reference was there all the time and they just didn't notice it. Or leave it to them to imagine it is one of the improvements you introduced and be happy about it. I would not make any further effort highlighting the reviewer's mistake, given that nothing hinges on your proving your paper right if you are not trying to appeal the rejection.
You might want to have a look as to whether you can reword the one sentence with the reference, just in case the respective reviewer could have reasonably interpreted the reference to be something else than the source/proof of claim X. Of course, be careful about this, because it brings the danger of making the sentence misleading to other readers who did not have any trouble interpreting the current version as it was intended to.