I didn't open the link you posted but I think I know which one you're talking about. What you have to remember is the FAA does not consider the CFI a pilot certificate. The whole no medical thing thing and so forth.
The flight review is a look at your flying skills to see if you've picked up bad habits in the last couple years. It's not a pass/fail event. If you added a SES rating, that would serve as a FR since your flying skills were checked during the ride.
The CFI checkride, either initial or renewal, is to see if you can teach. Yes, you have to be able to fly the aircraft to teach it. But in the eyes of the FAA, they are two different skills sets and take two different events to evaluate.