By taking the public relations offensive, the Russians have time and again been two steps ahead. U.S. and Western officials, not to mention the Kiev government, are left scrambling to debunk the rumors and fear-mongering. As a result they are frequently playing catchup for hearts and minds in the east.
How do you understand the phrase in a bold-type font? Does it mean that they take them (the public relations) as an offensive thing, they perceive the public relations as an offense to them?