Depends on circumstance of course, point was that Mistake is cognized in Law and if demonstrably a Mistake, for example ambiguous language interprable as admitting one's own work as "prior art" when its demonstrably not, a remedy could be effected. Prior art is prior art. An admission that non-prior art is prior art can't convert non-prior art into prior art.
Admissions, and in particular admissions of facts contrary to the speaker's interest have special legal significance. Remaining silent in the face of the examiner's statement against your interest can consitute an admission. Admissions against interest can be used against the speaker even when they aren't any good against anyone else. You may find yourself working very hard to overcome an admission, and in some cases, you might be legally precluded from challenging an unambigous admission.
Also consider the standard of review once your case gets off the examiner's desk. If the review is simply whether examiner's rejection is supported by substantial evidence, your admission *is* evidence that the examiner is entitled to rely on. He doesn't have to even bother providing evidence of facts that you admit to.
Otherwise, unscrupulous persons could file long specs in which non-prior art is alleged as being prior art, and assert the publication to have bearing on patentability of other cases filed just subsequent thereto. For example, Caligula hears that Prickter and Grumbly are working on a new paint composition including modified soybean oil but haven't yet filed an application. Caligula writes up a spec that states in the Background section that modified soy in paint (however modified, at various concentrations, and in various types of paints) is prior art and requests early publication. The spec publishes with a filing date earlier than Prickter's app.
A statement made by an unrelated party is not an admission with respect to the first parties case. But that may not matter here.
Cal's spec contains info about soy in paint, and an assertion that the info was known prior to Cal's filing. If the spec contains enough detail, the soy in paint info correctly gets a 102(e) date even if the statements that soy in paint was known prior to C's filing date are not accepted. Prickter and Grumbly may or may not be able to swear behind the 102(e) date or show that the info came from Prickter and Grumbly to begin with. If they cannot make the required showing, then they may not get a patent they actually deserve.