As someone who also ran a similar test myself and haven't seen a bit flip, I'm also skeptical of the 96% figure.
I'm too lazy to run the exact numbers right now, but with "4 GB, 96% percent chance, three days" as the hypothesis, I think you'll find that an experimental result of "8 GB, 0% chance, 14 days" is highly statistically significant.
Edit: rough back of napkin estimate - you're not seeing an event in roughly 10x trials (2x number of bits and ~5x number of days). Given hypothesis is true your experimental result has a probability of (1-0.96)^10 = very very small. Conclusion: hypothesis is false.