That *is* the "starter course", they just used regular 3-tab shingles flipped around backward with the slots up. Does the same thing as a "starter course strip".
Just to further clarify, the starter course in the diagram IS a regular full shingle turned 180 degrees, AND THAT IS WRONG.
The correct installation does not use the full shingle turned backwards, that is... well backwards, and does not follow the installation instructions provided by any manufacturer that I have seen. That is the standard practice around here, but that does not mean it is right.
That installation is more prone to wind damage since the self-seal strip is at the top of the first course instead of at the bottom edge like the manufacturer instructs.