The More Tag Protection functionality come into effect when the Title of the Post or the More Tag itself is clicked.
The member is able to view the entire Post (or the user is redirected to the Non-Members page if they do not have Access to that Post) if the title of the Post or the More Tag is clicked.
When the Posts Widget appears on the sidebar of a site, the titles of the Posts can be viewed. Clicking one of those titles is just like clicking on the More Tag.
Note that a Categories Widget could be placed on the sidebar and this would display the Categories.
A Category could then be clicked on which would show the list of Posts within that Category. This would display a list of Posts with the teaser text above the More Tags.
More Tags only appear in lists of the Posts.