I don't know what the question means by "Putin's Russia" but if President Putin and his administration did not try to influence the media it would be the only government administration that did not. Russia has the official Russian News Agency TASS, and I assume their writers are paid and that President Putin has influence over them. Whether President Putin's administration actually has writers in other agencies on the official payroll or pays them through a third party I do not know, but such accusations have been made.
In the US and much of the West, manipulation of the press by the national government is a little more subtle, since most countries do not have an official government news agency, but it is still very much a part of the domestic and foreign policy agenda. It is also a high priority among the major political parties and their large donors and supporters. However, even with the manipulation of government, the independence and strength of the press as the "Fourth Estate" to inform citizens in a free society is still an effective safeguard against government abuses. In the Internet age, some see independent bloggers, non-mainstream media outlets, and even the posting of mobile phone videos on the Internet as the emergence of a "Fifth Estate" to inform people. All governments are subject to more scrutiny because of the easy access to ideas and images over the Internet. However, as the Internet is often unfiltered, there is a lot of misinformation out there, also. One has to be discerning when evaluating any media outlet for information, formal or informal.