Not exactly. The current Alabama law says that the Alabama SOS must put on the ballot any Presidential candidate nominated by a "national party." So a more accurate formulation of your point is that the Dems or Repubs can put Putin on the ballot and neither the Alabama SOS nor the citizens of Alabama can do anything about it (except vote against him).
Yeah I know...The Dem Commie or the 'national' Rem and Stimpy party could put a thinly disguised Fidel C. or Stalin on the ballot, and they would vote for them. I also figured you would point out that little detail.