Am I missing something?
Yes.
So it does not use the voltage divider rule in this case?
It does not use the 'voltage divider rule'.
Ohm's law only applies to linear devices such as resistors, not to active devices such as Op-Amps which is essentially what an LM317 is.
The "voltage divider rule" is nothing more than Ohm's law applied twice.
If Vin is the voltage applied to the series combination of Ra and Rb and Vout is taken from across Rb then:
The first application of Ohm's law applied to the entire circuit tells us that the current I = Vin / (Ra + Rb)
The second application, applied to Rb alone, tells us that Vout = Vrb = I x Rb
Put these together and you get Vout = (Vin / (Ra + Rb)) x Rb
Rework these mathematically to get the version you are used to seeing
Vout = Vin x Rb/(Ra + Rb)
In my opinion you are better off forgetting the rule and learning how and when to apply Ohm's law.
Don