First off, every time you sign-in the check box is checked by default. Even if you sign in and out- the web page remembers your accounts but will not remember your preference for staying signed in.
Second- if you are signing in and un-check the box but mistype your password the page reloads with the checkbox re-checked.
Third- Since you now are back at this screen and may want to un-check this box again, the tab order is now altered. Before you could simply tab twice past the password box and hit the space-bar to un-check the checkbox. Now a link is in the way- if you tab twice and hit space-bar it will sign you in with the checkbox checked!
All of these seem kind of trivial for most users. Most people want to stay signed in on their personal computer. But for me and many like me I need access to my email from computers that are not my own. For me, having additional ways for my account to accidentally persist its session are cause for concern. Considering that Google probably has large team of people to think about all these scenarios it is also apparent that these changes were intentional to have the user stay signed in as much as possible, even if by mistakte.