Edit: Ah, it's because the phone was in silent mode. That usually doesn't prevent website sounds playing. Not sure what's different here.
I've noticed that 1) silent mode and 2) not wearing headphones sometimes causes the muting, but I'm still trying to figure out why exactly some iPhones seem to play fine with headphones and why some iPhones require headphones.
Edit: Ah, it's because the phone was in silent mode. That usually doesn't prevent website sounds playing. Not sure what's different here.