On some websites, the overlay can't be closed easily. In that case, it's not hard to open the DOM inspector and delete the overlay, allowing you to see the "hidden" text.
Unfortunately this has to be done fairly regularly. So, thank goodness, somebody out there has created extensions to automate this.
Chrome:
Firefox:
If you want an example to test with, load >4 stories from this site. Or go to Pinterest while not logged in, and try to access any user's content.