I have just checked with the Civilopedia stating that the Persian Immortal is to move 2 hexes.
In my current game, it moves 2 hexes and still attacks me.
Bug of the Civilopedia or bug of the unit?
Attached savefile plays on a huge map with standard number of civs and CS. So, it may not run well on each computer (although being in turn 87).
It would be so easy to find the right autosave if it wouldn't take ages to load. 
How to reproduc:
In my current game, it moves 2 hexes and still attacks me.

Bug of the Civilopedia or bug of the unit?
Attached savefile plays on a huge map with standard number of civs and CS. So, it may not run well on each computer (although being in turn 87).


How to reproduc:
- Bombard the Pasargadae with the archer right of it.
- Take the city with the adjacent horseman (horseman 1) and make a puppet state.
- Capture Persian settler with the horseman (horseman 2) right of the immortal (lower edge of the screen).
- Kill Persian General with the scout.
- Move crossbow to the north
- Move archer SE (3) of Pelzbach to (4)
- Move archer (!!) NW of horseman 2 SW (1) upon the connecting toad between Persepolis and Pasergadae.
- Let the warrior next to the Barb village wait. Promote the archer with whatever you want.
- Let the next turn start: