Why does a resistor need to be on the anode of an LED?
The resistor can be on either side of the LED, but it must be present.  When two or more components are in series, the current will be the same through all of them, and so it doesn't matter which order they are in.  I think the way to read "the resistor must be connected to the anode" as "the resistor cannot be omitted from the circuit."