I was under the impression that once you've set your password against your Standard ID, this password then replaces the locally stored password for the user containing that Standard ID, thereby allowing users to log in with their Standard ID and password, or Person code and same password if there is no connection to the Standard ID password server. Is that still the case?

Is the problem here that multiple people are using the same client? If not, it does remember the e-mail address of the last user to log in, so it's not really a problem.