Sure, but at the level Russia can afford, and "puppeteering the US president" is a BS claim way above that, tailor-made for a nation spoon-fed with shows like 24 and Homeland and endless claims about how all the world "plots against it" while itself does exactly that globally (and nobody bats an eyelid).

And while Russia/Putin will use such tactics for their country's (and/or his own) immediate interests/survival (e.g. in Crimea, a place with a huge majority of ethnic Russians, or the middle east), they don't have neither the means or the history of meddling and plundering all over the world.

The claims are mostly a way to invent a present-day Bond villain, an easily identifiable target, like it has been played out tons of times in the past. Russia has too many natural resources and wants to control its periphery, something that goes against the general "interests" and plundering intentions of outside players, hence the pressure, combined with the constant post-Cold-War expansion of Nato to suffocate them.

If instead of Putin there was some friendly dolt selling Russia wholesale to foreign corporate interests (instead to national players that the country can somewhat control -- something which is labeled "cronyism"), like e.g. Yeltsin, it would be all love and hugs with EU and the US, even if they did ten times worse in freedom internally. You know, like those lovable Saudis.