Second things first. Simply modifying a PDF file's modification date by itself would not cause Acrobat to attempt to repair a PDF file. Whatever hacking tool modified the file's modification date must have also modified some internal aspect of the PDF file. If such files were previously known to open without any issues (i.e., attempting repair and then prompting to save when closing), then regrettably, you much assume that the hacking tool may have compromised your PDF file in some manner that might not be immediately obvious. Did you try running any virus scan against the compromised file server volume? In any case, I would do whatever I could to restore the server's volume from a backup. What you/we don't know about whatever changes were made to your files could really come back to haunt you later. There could be time bombs in there.
In terms of the report generated by Generate System Report, that is effectively a system configuration report, nothing more and nothing less. Depending upon when it is run, the list of plug-ins could range from a few to many. Acrobat doesn't load all its plug-ins at start-up; some are only loaded on demand. It is somewhat suspicious that no plug-ins show when the hacked PDFs are opened. That having been said, what shows in the dialog box isn't the entire report. Have the report sent to your own e-mail address and examine the results. If you want, we can take a look at it if you post the file somewhere.
- Dov