NATO forces could be used against the governments of European states which take decisions that go against the US’s wishes. This idea is supported by The New York Times, which is the mouthpiece of the US “deep state”. The Armed Forces of NATO member states obey orders issued by the US military command.
This message is consistent with a basic pro-Kremlin disinformation narrative on US relations with EU countries. Pro-Kremlin outlets often allege that different countries, America's transatlantic allies in this case, are US vassals and remain under the American thumb. See earlier examples: Poland is US's vassal state, Europe is occupied by the US and has limited sovereignty, the EU is directed by Washington, Germany is the executor of US hegemony over Europe.
NATO is a political and military alliance, and NATO member states make sovereign decisions about their own security. NATO and US military presence in these states is possible only on the basis of the clear consent of the hosting nation. Moreover, all NATO decisions are made by consensus, after discussion and consultation among member countries.
The New York Times article referred to by Sputnik discusses recent military exercises in Eastern Europe, involving US special forces - and the special forces of several Eastern European states - aimed at thwarting hybrid warfare operations [that is, operations that involve a mix of subversion, cyber-attacks and information warfare].
For other disinfo cases related to NATO see here.