That's the Dungannon to which my da was referring.
The phrase probably came from some drunken conversation.
I don't know Dungannon that well - spent one drunken evening in a wee pub there (McGrath's?) where my sister was playing with her two-piece cabaret outfit. Followed on from an earlier all-afternoon barbecue in Lurgan. Myself and my uncle Henry and my ma went along for the crack. My ma got a bit worried when I decided to sing "The Oul' Orange Flute", which I thought was apt, given that we were in Dungannon. Can't remember too much else about the night given that it was the end of a long, hard day's drinking. (Something which doesn't feature as highly on my list of priorities these days as it once did!)