I tried this in demo (together with Mirko Trinajstic): I created a new invoice with date 11/01/2014 (Period November). I used the standard payment rule "Check" as it was. Then I completed this document and checked the postings. All postings were done with accounting date 11/01/2014 (as expected). The Accounting date of the Document is the same: 11/01/2014. This field is read-only.
Then I changed the payment rule to "Cash", saved that and pressed the little button near "Cash". In the window I set a date 12/01/2014 (December). After finishing this window the Accounting Date of the Document changed into 12/01/2014. The postings still are the same than before.
As a result the accounting date of the document is not the same as the posting dates.