I have definitely heard of a break being missed on an initial x-ray. I broke a vertebrae in my lower back in 2011. When the break happened I felt no pain (I'm one of those lucky ones that doesn't get much or any pain with broken bones, just feel nauseous and gut feeling knowing something is broken), but I could tell something was very wrong. My boyfriend immediately took me to the ER where x-rays were done and showed no break, the doctor said it was only a sprain and I could ride the next day (wish I had gotten his name, I landed on my head and cracked my helmet open, and was also told my same doctor I "likely sprained my neck", yet I can ride the next day. Yea, definitely wish I had that name, and thank god I didn't actually ride the next day
) 5 days later something was still very wrong, so I went to my family doctor where he correctly diagnosed the break/slipped disc/neck sprain/concussion.
My best friend also had the same thing happen, only she broke her knee and initial x-rays said she was fine, then went back ~2 weeks later when it wasn't feeling any better and turns out she had broken it.
Apparently mis-diagnosed breaks are more common than one may think. Before my mum worked in Oncology she worked off and on in ER and ...something else as well? Anyway, she saw a lot of people come through that had on their chart saying something along the lines of a break being diagnosed after second x-ray, too much swelling on the first x-ray. That sort of thing. So yes, it happens.