Great topic, everyone. Thanks for bringing it up, Scott, and Ron and Jesse for providing the answer. Now, I can add the justification, and more about the internals of Fusion than you probably ever wanted to know.
So, the obvious question here is: Why don't we show a coincident constraint at the corners of a rectangle? Mostly it's for clutter control. Can you imagine what a sketch would look like if every junction had a visible coincident constraint? So we made a rule: Don't show coincident constraints when there are two or more lines sharing the same endpoints. Also, because we are fussy technical types, we did this because it reflects the internal data model as well. When you create a rectangle, there are just 4 lines and 4 points involved. That is, the 4 lines "share" an endpoint at each end. There really is no coincident constraint there. We could have implemented it as 4 lines and 8 points, with coincident constraints between pairs of endpoints, but then the data model gets messy, and there are more points and more constraints to deal with internally as well as externally. For what it's worth, this is the same implementation as in Inventor (most of us worked on Inventor too).
But, then, sometimes (like in this case), you do want to pull apart the rectangle. So, that's why we put in the "Delete Coincident" command into the context menu. (and, just FYI, Scott, you can get this command on a selected line as well as a selected point, like Inventor, and it is sensitive to what end of the line you selected). This command makes it look like you are deleting an invisible constraint, but what is really happening is that we are adding a new point to the sketch, and pointing one of the lines to it. If you select the point to do this, we just pick one of the lines (if there are more than two sharing the same point), if you select a line, then it's obvious. The points are then on top of each other, and if you drag one off, the lines will separate.
If you drag one point on top of another, the inverse happens: We merge the points. So, if you are not careful how you drag you can: 1) Delete Coincident 2) drag the points apart 3) drag them back together, leaving you exactly where you started.
Fusion does not merge the points if they just happen to sit on top of each other for other reasons. For instance:

The result is two points sitting on top of each other. Yeah, probably too much information...

The last interesting thing that is somewhat related: In Fusion, you do not have to have the coincident constraint for Fusion to recognize a profile:

Hope this was enlightening in some small way
Jeff Strater (Fusion development)
Jeff Strater
Engineering Director