double post, sorry.
Edit.
From more technical point of view, the reason for time drift has to be searched in Arduino core sources.
The millis() function is defined inside wiring.c file located in the IDE installation folder ..\Arduino\hardware\arduino\avr\cores\arduino
As clearly written in the comments, with AVR MCUs like the ATmega328p of Uno R3 board
// the prescaler is set so that timer0 ticks every 64 clock cycles, and the
// the overflow handler is called every 256 ticks.
#define MICROSECONDS_PER_TIMER0_OVERFLOW (clockCyclesToMicroseconds(64 * 256))
With a clock of 16Mhz we have that duration of a single cycles is equal to 1/16.000.000 = 0,0000000625 seconds
So Timer0 will overflow every 0,0000000625 * 64 * 256 = 0,001024 seconds that is to say millis() will increment of 1 every 1.024 ms.
This is why millis() is not a good choice for accurate time keeping