Their belief didn't make the accounts come true, and they certainly didn't witness them. In effect, you are believing something highly unlikely simply because someone else did.
Why don't you do that with things you hear about today?
Try this little exercise for yourself:
Take any story you like from your holy book - stories about what the prophets did or said, or about what different tribes of people are said to have done, or stories about what a god allegedly said to someone - preferably stories which form the foundation of your faith but not necessarily so.
Now, imagine someone passing along your street told you that this event was happening right now, or had just happened, a mile down the road. Would it make any difference if this person wrote it down? Would you believe them or would you think they were deluded, mistaken or lying to you for some reason and probably selling you something?
I suggest that only the most gullible and credulous of people or the insane would believe these stories without at least asking to see the evidence, if they were reported as happening today.
Yet the people who wrote those stories down in the Bible or the Qur'an or other holy books either believed people who told them they had happened or expected other people to believe them without any available evidence. And that's exactly what you've done, if you believe those stories are actually true.
How is that different to believing the person walking along your street? More to the point, where does it leave your faith if you have no rational basis for believing the stories in your holy book?
Try the little exercise above and let me know which stories you would believe and what would convince you to take the word of a complete stranger that these extraordinary events were taking place just down the road today, without needing any evidence.