Calibre does not sync books. It does sync metadata if metadata management is set to automatic, but that process will not change the file date of the books (or at least, I know of no way that it does). And in any event, the process is identical whether or not a book is added.
I suspect that in this case, the 'sync' happens when the device is ejected. At that point, the reader will scan every book in memory, comparing information from its database to the information in the books. This is a mysterious process, out of control of calibre.
The thing to do now is run calibre in debug mode to see what, if anything, calibre is doing. If you are using windows, then open a command box (start, run, type cmd, press OK). Note the current folder; it will be listed in the prompt. With your 300 not connected, type
Code:
calibre-debug -g > caldebug.txt 2>&1
Calibre will start. Plug in your 300 and send 1 book. As soon as everything finishes, quit calibre. You will then get another prompt in the cmd box.
Open a file explorer and go to the folder you noted earlier. There should be a file caldebug.txt in that folder. Look at it to be sure that there isn't any private information in it (names of collections, book title, etc). If not, then post the log here.