I think I found an answer for all my doubts and I am sharing it here:
According to this video: https://www.youtube.com/watch?v=5mf4NmmLWnE when the the battery to the motor is on, and the armature is spinning we have both rules (right and left hand) acting simultaneously.
The right hand rule "generates a current" (actually a voltage) in the opposite direction of the applied voltage by the battery, but it is weaker then the battery and the resultant voltage is positive (thus keeping the current going forward and not reverse). This is called back emf.
Here is another great explanation about back emf: https://www.youtube.com/watch?v=5XcWJa9JBuY
If the motor uses a permanent magnet, then if we cut the applied voltage, the motor will continue to spin due to inertia and only the back emf will remain, thus the back (negative) voltage will generate a current in the opposite direction and our circuit needs a protection.
But if we are using a DC motor that uses electromagnet instead of permanent magnet (as the motor used by Adafruit in the question), then the motor basically have an inductor inside it. This inductor (the electromagnet) can be connect in parallel (shunt motor) or in series as explained here: https://youtu.be/LAtPHANEfQo?t=158
As the inductor tends to keep the same current flow, when you turn off the applied voltage this inductor will try to keep the current in the same direction acting as a generator. And this inductor is usually stronger then the back emf, thus not causing a reverse current.
So in the schematic presented by Adafruit, the diode only protects against the inductance inside the DC motor. It doesn't protect (and it doesn't really need to protect) the circuit against reverse current unless some mean person spins the motor while it is off.