Show me some science backing up this crazy belief that running with headphones is more dangerous than sitting on a sofa watching TV while eating a bag of chips.
We're comparing running with headphones vs. running without headphones, not running vs. sitting on couch eating junk.
Here's the study that produced the figures mentioned a few posts above. Headphones are definitely an extra risk. We may choose not to be worried by that risk and we can say it's small compared to other risks, but let's not say the extra risk is zero, because that's false.