....”The question remains why he would lie about moving them when their presence and lack of movement can easily be verified?”......
No...there is no question... it doesn’t matter what Putin says regarding the troops...he has a right to move them when and how he wants on his border, especially with a War-Zone in Eastern Ukraine, his border state. Further it was ‘understood’ whatever mass withdrawal, if any, would be within 24 hours minimum.
Most recognize the communication ‘being reported’ between US and Russia isn’t exactly trustworthy at this time, as the deals etc. are surely going on behind the scenes.
The war-zone is due to Putin’s manipulations of the criminal element in those cities. That’s why Rinat Akhmetov has stepped in.