Is there any way to "shake off" undesirable statements made during the prosecution of a patent?

Yes. Consider a continuation application, for example.  If the patent applicant makes a statement that the statements/admissions made in the parent application do not apply to the current claims, those "disclaiming" statements would likely be honored.  In most cases, courts reading file histories try to act reasonably, and will not woodenly apply "rules" on this kind of issue.