Of course in this day an age, having any kind of job is a victory in and of itself. Which is how I rationalize Water Cooler Chris' eventual demotion.
I'll bet he let it slide and pretended his name was "Speaking." That's what I would've done. #awkward
Or four-ply. Or eight-ply. Sixteen? Let's not get carried away.
If his headphones are in while you're serving him, then it's both.
It isn't the waitstaff's only job to serve you. They're also interpreters that can skillfully translate a wide variety of awkward-speak.