Suppose you want to measure the distribution of the delay between recurring events (which is basically what's at the heart of those vulnerabilities). Suppose the delays are all sub-milliseconds, and that your timer, to pick something ridiculous, only has a 2 second granularity.
You may at first think that you cannot measure the sub-millisecond distribution with such a corse timer. But consider that event and timers are not synchronized to each other, so with enough patience, you will still catch some events barely on the left or on the right side of your 2 second timer tick. Do this over a long enough time, and you can reconstruct the original distribution. Even adding some randomness to the timer tick just means you need more samples to suss the statistic out.
Again, I am not an expert, and I don't know if this actually works, but that's what I came up with intuitively, and it matches with what I heard from some trustworthy people on the subject, namely that non-precision timers are not a panacea.