Both. I just got my replacement and its doing the same thing as well.
Here's a video. Is this a general issue?
I don't think it's an issue, actually. I think it's part of palm rejection.
Try this: instead of tapping on the edge, put your finger anywhere on the trackpad but not close to the edge, then drag your finger accross the surface to the edge - and try to click.
Works, right? For me it works every time. Because no one really starts dragging and clicking from the edge, but we sometimes end up dragging something near the edge. And in this case it always works and you can move and click at the very edge - as long as you don't start there.
So, I think this is part of a system to prevent accidental palm clicks when typing.