Don't have a Moodle exhibiting the same issue so consider the following un-tested and really un-known, but, hopefully, will get you closer to resolution:
In the database for your Moodle, mdl_assignment_submissions table:
There are three fields related to time: timecreated, timemodified, timemarked. All of those use UNIX epoch time.
UNIX epoch time example: 1229573101
Using a site that converts into 'humanly understandable':
http://www.epochconverter.com/
Copy and paste the number above.
Will return this:
GMT: Thu, 18 Dec 2008 04:05:01 GMT
Your time zone: Wed Dec 17 22:05:01 2008 GMT-6
There are also fields for 'assignment' (a number so assume that is the assignment ID number) and user id (probably student). Use the mdl_assignment table to cross reference.
So a query like:
select userid from mdl_assignment_submissions where userid="52";
should show that students assignment submission data.
One could then edit the time fields to taste (it is thought). Just to be safe, record what data was in there to something like notepad/textedit/a true text editor before replacing.
Assume have some tool to view/edit the database ... like phpmyadmin.
Do a database dump ... ie, backup your database ... *BEFORE* trying anything.
'spirit of sharing', Ken