Well it can't be a coincedence and more importantly it is logical and here is the possible explanation/illustration , The following steps assume that you are online and that the Kindle for PC is installed but the application is closed/not active within Windows!!
Firstly download a free $00.00 Kindle ebook from the Amazon kindle store eg.
http://www.amazon.com/Weekly-Menu-Pl...848536&sr=1-40
Secondly make sure you have DELIVER TO to "your name" Kindle for PC then press Buy with one click, thus the transaction goes to a second thank you webpage where a button appears and states GO TO KINDLE FOR PC
Thirdly as you press the above button (remember that the PC Kindle application was closed/inactive at the beginning of these steps), you suddenly see the main window of Kindle for PC appear as well as it downloading/sync the free ebook example.
Fourthly and lastly it appears that the Registering/deregistering Amazon Kindle webpage and the Kindle for PC software are linked in the background and thus possibly it needs to have online access when one is installing or uninstalling the software. Good luck