Might be wrong, but don't think the error means Moodle is attempting to send X amount of data at Chrome, but rather, Chrome's ability to change/update data on local machine. First poster's 'data' is different than what you've reported - the size.
Yes, the fact this is happening with Student accounts makes it a major issue. So in just your case, are all students accessing your Moodle from the same LAN/WAN or are they remotely accessing with the 'recommended browser' for the site?
Howard asked about plugins ... got any?
'spirit of sharing', Ken
