mmm, now how is the person who has had the finger pointed at normally, do they have a tendency to over step their job description.
Because when someone asks for the person they have mentioned as upsetting them not to be approached, it could be that they have put a bit of a spin on what happened.
Mrs. T is correct you should of said I will talk to them about it,
You do need in a none confrontational way find out the other side of the story,
The other employee may of called this person out on some sort of slacking, and followed up with, You don't want Inky to think you are slacking, and that got turned into for your benefit, Inky thinks you are a slacker,
Have a meeting with the other employee, go through appraisal of their work and job description, listen carefully to any concerns, reiterate very carefully what you want from them.
Then keep a far more careful eye and ear on what is going on.
I won't have anyone I do not trust explicitly working for me.