You have to fly the assigned Mach. You look at the CMA's (Control Monitoring Agency) write-ups of crews and see this violation occurs frequently. How you fly your assigned Mach is essentially only one of two ways: a) either hard line it in the FMS or... b) Speed Intervene and open the speed window. If you were to select B, you lose the ability of the time forecasting for each point.

If your Chief Check Airman told you it had been approved, he's sadly wrong. You can go into the NAT PCO.org page and look at each working group and the material they are working on. There is an evolutionary time frame for the NEXGEN where they want the controller to be able to adjust the MACH as needed to increase the e number of planes on the tracks. Your Check Airman is way off the mark. You could contact the NAT group or the FAA rep and ask for his opinion on it, but your interpretation is correct.