This isn't true for all tapes. It should measure correct when used this way, but the ends are notorious for being inaccurate.

You can see the inaccuracy in the photo. Use a photo editor or a post-it on your screen and grab 1/2 inch from further down the tape. Move it down to the end and you'll see your 1/2 inch reference line up with 9/16th.

Summary: it's 1/2 inch board. The tape measure is off by a 16th, like you said.