Not to beat a dead horse, but to reinforce what Ana was explaining oldbroad.
What you are experiencing is only specific to your computer because of a function that is used on many website with logins called a Persistent Login and sometimes use a tool called a persistent cookie. Both are functions that can only occur on the person's computer who logged into the respective account. In many websites, that function is activated when you check a box that says something to the effect of "Remember Me." Amazon's Persistent Login function is different and strictly regulated.
Your account information is stored, temporarily and only your browser will access it. Some such features have an expiration date attached so they no longer have your account information stored after a certain period of time.
Amazon's persistent login is very specific and separates certain identifiers from those that would be normally considered secure. It will allow you to access your account without needing to login, but only for a short period of time. After that time expires, if you haven't cleared your caches and/or cookies, you will still have a personalized experience the next time you open the Amazon site.
It will say something like, "John Smith's Amazon" BUT if you try to access your orders or more depthy information it will require a password.
Secure information cannot be transferred through the normal means of copy/pasting an item link.
"A world is supported by four things: The learning of the wise, the justice of the great, the prayers of the righteous, the valor of the brave, but all of these are as nothing without a ruler who knows the art of ruling - Make that the science of your tradition."
The Reverend Mother Gaius Helen Mohiam from the novel Dune