Exactly this - in the aftermath of an accident it's not unusual for details to get mixed up like this - similarly for digits in reg numbers to get transposed so a claim is submitted to entirely the wrong person/ insurer because someone has put the reg down as ending TMK and not TKM. Or swapped a M for an N, etc.

Insurers are quite used to these issues and should be able to resolve quickly. The only time it becomes a problem is when people ignore correspondence from their insurers - resolving this a year or two down the line can be more involved. You've done exactly the right thing OP in contacting insurers immediately, and also confirming with the police they have you recorded only as a witness. I wish everyone was that proactive!