On a public post on Facebook, McDonald's wrote: "Well done with the old phone number swap. You got us good. We're telling people to complain that you're giving away free burgers tonight - so let us know if that's not the right message for your callers. [smiley face].''
In turn, Ekim Burgers replied that they would let customers have a decent burger and suggested giving away free fries as well.
Tonight, Mr Duffy told the Herald he was not behind the phone number swap.
"It could've been anybody. I have access to it, yes, but so do a lot of other people in [my staff].''
Mr Duffy said he was looking at getting someone to have the phone number removed. But at the moment, he was still having to deal with "crazy'' people.
"It's ridiculous. There are some really angry people out there.''
A McDonald's spokeswoman confirmed the post was legitimate, but played it down as banter between two food places.
"It's just a bit of fun on our part. There's nothing serious in it.''