Math I think your admiration for Putin (iirc related to his hostility towards Muslim militants) blinds you to what is going on.
BigChoc, I think you are seeing Russian boogeymen to such an extent that you cannot appreciate the fact that the fake news phenomenon arose from the 90s culture wars in the US, and that it is a homegrown phenomenon that needed no fuel from anywhere in order to ignite it. What set it alight in the US was the election of a black president, a completely intolerable event in the eyes of racist America, and proof that the apocalypse is upon us.
The right wing is alive and kicking in the west, in South Africa and in NI and in the American South, and also in western European countries like France, Belgium and the Netherlands and it was not Putin who nurtured it. In the east and central Europe, Hungary, Slovakia, the Baltic states, Croatia and western Ukraine have always played with fascism and have had home grown fascist movements from the inter war years onwards. Many regimes in those states were openly supportive allies of the Third Reich. Even Poland had a flirtation with authoritarianism before WW2, and some fringe fascist movements. Italy of course contributed the name itself.
The UK is heading in this direction with virtually nobody able to see it or apply the brakes. Is this Putin's doing too? Or have the Tories always been latent right wing authoritarians and Little Englanders? Regulation of industry, elimination of safeguards like the ECJ or the ECHR, and rhetoric that is hostile to immigrants, calls for national unity, etc., are all either present or gathering speed in the UK.
If a rift between Europe and the US is Putin's goal then he requires a European entity and not a vacuum in order to make that scenario operate to his advantage. Destroying the EU is not Putin's aim.
Russia's involvement in effectively mopping up after the catastrophic destabilisation in the ME caused by rash and illegal British and American adventures there has so far prevented Israel from pushing the nuclear button, and Russia's alignment with Iran (which has also contributed forces to fight ISIS in Syria) has so far prevented the US from doing likewise. This is even before we get around to mentioning the liberation of millions of Muslims from the brutal rule of the ISIS fundamentalists. What's not to like? Would you prefer to see ISIS overrun the entire middle east? Nuclear holocaust? What is your problem with wanting to wipe out Muslim militants who want to destroy the west?