There are several possibilities. The examiner could simply be misusing a form on the PTO's database. OR, he could be genuinely confused as to whether a new ground of rejection exists (e.g., he changed some words but not the substance of the rejection). OR, there might be a new ground of rejection, but the basis of the new ground is nuanced and you might be missing it.
Is the examiner allowing you to reopen prosecution without filing an RCE? If so, that suggests to me that either: 1) you are dealing with a very junior examiner who doesn't know what he/she is doing; or 2) the examiner or his/her SPE s not confident in their grounds of rejection.
Regardless, my suggestion is to call the examiner and ask him to clarify the basis of the new ground of rejection. If it's a mistake, I would file a response to examiner's answer (and the required interview summary), noting that the new ground of rejection is in error.
As to whether, as a general rule, a practitioner should respond to an examiner's answer, my answer is "YES . . . and no." I typically always respond to examiner's answers, simply because I don't want the examiner to have the last word, and so that there is no possibility that the examiner raised arguments that were not addressed on appeal. But in cases of examiner error, it sometimes comes down to a cost/benefit analysis. I.e., how much it would cost for you to draft and file the response, versus how much benefit is likely obtained from filing that response. If the examiner made a min ior error that was obvious on its face, there is probably little benefit to be gleaned from ffiling a response solely to correct that error. But in your case, the examiner is alleging that there is a new ground of rejection, which may (however unlikely) confuse the board that there is an outsrtanding rejection/argument that has not been addressed by the applicant on appeal. APersonally I think taking the time to correct that error/misrepresentation is worth it on appeal, if for no other reason than you avoid the possibility of distracting the board with extraneous issues.