It's possible the dig at OKC from Maynard James Keenan might be from OKC's strange position in recent years of getting skipped by many rock band tours. Over the past 10-15 years I've noticed a great deal of popular music acts playing Tulsa venues like the BOK Center or Cain's Ballroom but not having any dates in OKC at all.
The Paycom Center (aka Chesapeake Arena & originally the Ford Center) where the OKC Thunder play rarely ever hosts rock concerts. I did see Nine Inch Nails play there in 2007 (awesome concert; they made a Blu-ray concert video from the show). Most other arena-sized concerts I've seen in OKC have been at across the street at the Myriad Convention Center (later called the Cox Convention Center). I watched a decent number of minor league hockey games there too. That arena opened in 1972 and was showing its age 20+ years ago. The venue is now being turned into some kind of a movie/TV production studio.
The OKC live show situation has a lot of moving parts to it. I believe Paycom/Chesapeake doesn't host concerts very often because the Thunder's lease dictates a level of access that ends up being incompatible with concerts in practice. Many of the remaining venues in town are owned by groups that also own the venues in Tulsa, and when they are given a single date, for some reason they prefer to schedule it in Tulsa. Must be more profitable for them somehow. Or the companies are just run by Tulsan homers.
Unfortunately for the venue owners, the city is maturing to the point that they now have people coming into money in OKC saying "why doesn't OKC ever get good concerts?" and opening new independent venues here to break the logjam. As a result the OKC concert-going crowd is starting to sour on the idea of driving the 90 minutes to Tulsa to go to a show. "Eh...I really want to see X group, but their tour is only going to Tulsa...but the Jones Assembly here in OKC is having Y that weekend, and I've been kinda wanting to see them too..."
Does anyone living in Oklahoma actually call OKC "Oak City?"
No.
Dallas and Kansas City would be better suited for rock concerts, but who'd want to drive a couple hundred miles to either city just to see them play? Plus, Oklahoma City would be more in line with hosting country artists anyway (seeing that Carrie Underwood, the Season 4 winner of American Idol, is from Checotah, which is a stone's throw away to the east on I-40).
Bad take. There are more country fans in OKC than there are in other cities, but OKC is still a city, and by and large the population has just as diverse a taste in music as any other US city. Not putting on rock concerts here is simply leaving money on the table. The casinos tend to hold most of the country concerts, and that's honestly a better place for them since they're all on the outskirts of the metro and closer to the actual country.
Also Checotah is closer to Tulsa than it is OKC. I don't really know how that's relevant, though; they produced one artist. Otherwise, it's a fairly unremarkable highway crossroads town. Nashville they ain't. (And besides, if that was relevant, it would actually be more of an argument for OKC to hold more rock concerts; OKC produced the Flaming Lips, after all.)