Why do applications update when I have declined the Google Play terms of service? On my Samsung Note 3 I have declined the Google Play terms of service. Despite this, the system has connected to Google Play to download updates for all the bloatware preinstalled on the system, and a few other third-party applications such as JuiceSSH that I've installed.

By whose authority are these updates being made, after I've explicitly denied their terms?
Samsung has its own appstore: Galaxy Apps. The bloatware on my Galaxy S6 is installed and updated through that instead of through Google Play. Could that be going on on your Note 3? I don't know if Galaxy Apps updates apps installed through Google Play, but perhaps it does.