The international standard is that when required to maintain or where a pilot has informed ATS that they will maintain a specific speed then they are considered to be maintaining that speed when within 5% of that speed.
5% of 160 is 8Kt.
Thus 160 knots is maintained by keeping the speed between 152 and 168.
Yes in many cases we do better than that.
However, those are the allowances and in most cases, ATC would not know the difference between 160 and 165 with the changes in wind etc affecting groundpeed which after all is what ATC are really interested in.
If this ATCO has a problem with the speed being 5 knots high then he should have slowed the flight by 5 knots.
Sounds to me like an ATCO at TC who uses the selected speed readout of mode S and was not impressed by the selection of 165 when 160 had been requested.
Regards,
DFC