This is no nonsense, although the error is probably not very big.
Mach is the ratio between TAS and the speed of sound. The speed of sound depends on the temperature: a = sqrt(1.4*287.05287*T) (T in Kelvin, a in m/s ).
Mach meters that rely on altitude measurements for temperature derive the temperature from the ICAO Standard Atmosphere (ISA). In ISA, temperature of the atmosphere at sea level is 288.15 K, or 15 °C, and cools down by 6.5° for every 1000 meter you go up. Above 11000m the temperature is assumed constant, at 216.65 K, or -56.5 °C.
The differences between the assumed ISA temperature and the actual temperature can be quite big, but are usually below 20° deviation.
Example:
An aircraft flying is 400 KTAS at 30.000 ft, the OAT is -55 °C.
-55° C = 218.15 K
The speed of sound is: sqrt(1.4*287.05287*218.15) = 296.1 m/s, or 575.6 KTAS
The mach number is: 400/575.6 = 0.695
According to ISA, the temperature would be:
30.000 ft = 9144 m
288.15-0.0065*9114m = 228.7 K or -44.4 °C
The speed of sound is: sqrt(1.4*287.05287*228.7) = 303.2 m/s or 589 KTAS
The mach number would read: 400/589 = 0.679.
So for a ±10 °C deviation at 30.000 ft you get a misreading of ± 2.4%
Cheers,
ATCast