Stability and accuracy, when applied to clocks, are generally about dynamic range, i.e. how good is the scale with which you are measuring time. So if you're talking about nanoseconds across a long time period, seconds or longer, then yeah, you probably should care about your clock. But when you're measuring nanoseconds out of a millisecond or microsecond, it really doesn't matter that much and you're going to be OK with the average crystal oscillator in a PC. (and if you're measuring a 10% difference like in the article, you're going to be fine with a mechanical clock as your reference if you can do the operation a billion times in a row).

This setup is a user space program on a machine that is not exclusively dedicated to the test running all kinds of interrupts (and other tasks) left, right and center through the software under test.