At lower AC votages the small meter will be off even more. The 'rectifier' is just a silicon diode with its knee voltage not compensated. (try to measure 2V AC for instance)
It's why the smallest range is 200V AC to 'hide' this issue.
The Fluke probably calculates true RMS by taking the waveform in account as well.
Mains voltages generally are far from truly sinusoidial, they are flattened on the tops due to rectifiers in other equipment.
What the hell, let's do some quick tests with a function generator.
Sine wave, 50 Hz, varying amplitude
1 Vpp: Fluke 0.3522 Vrms, Cheapo 0.1 V
2 Vpp: 0.7035 Vrms, 0.4 V
5 Vpp: 1.7595 Vrms, 1.4 V
Not even close.
5 Vpp sine, varying frequency
100 Hz: Fluke 1.7623 Vrms, Cheapo 1.4 V
1 kHz: 1.7601 Vrms, 1.4 V
10 kHz: 1.7620 Vrms, 1.3 V
20 kHz: 1.7608 Vrms, 1.2 V
50 kHz: 1.6196 Vrms, 0.9 V
100 kHz: 1.1440 Vrms, 0.4 V
The Fluke covers the audio range, whereas the cheapo doesn't.