Medvedev is not talking about "rational democracy", you (and AFP) are. AFP glued together phrases from different parts of the interview and then invented "rational democracy" (once again,  never used by Medvedev) for the headline based on this chopped sentence.

"Managed democracy" is introduced by Tretyakov in 2000 for the description of Yeltsin's regime from 1993 to 2000, especially the Voloshin and Putin as PM period and referred to the state and oligarchs manipulating the political process using media, spoiler parties, defining democracy as power of the democrats and using authoritarian means were result from democratic process was not guaranteed.

Since then it was used for some time in Russian expert circles, but was never dubbed as official ideology. By 2003 it became mostly derogatory term  used by professional fighters with Putin "regime". At this point in time I'm not sure if the term actually describes anything and if it does, why I don't see why it is not applied to all of the new Europe, Italy, Japan, UK and US, to name a few countries.