I fear you are mistaken, and I cannot correct you because we are not informed about what files were accessed, or had the access dates changed, if any. Yes, I know about the 960 files, but we don't know where they were, what happened to them or in what order. The computer does NOT need to be on a network for this to happen at all.
Take, as an example, a couple of fairly common programs. Anti-Virus, and Google Desktop. Google Desktop is a program which resides ON THE LOCAL COMPUTER, and maintains an index of files, and the CONTENT of the file so that you can do a keyword search on your system. Have a file that contains Grandma's famous chocolate cake, but can't remember what you named it, or where you put it? This is the trick for you! It will be able to find all files that have "Grandma" or "Chocolate" or "Cake", even if they are in e-mails, etc. To work this magic, the software runs in the background and searches the contents of those files to build the search index, and, you guessed it, in order to populate the index it has to read the file so it gets the contents of the file.
Anti-Virus software usually scans at regular intervals, but it depends on the settings. Some programs will realize that they have missed one or more scheduled scans and begin scanning as soon as the system is turned on, which again changes the access date of the file. Note it changes the access date, not the modified date.