One of the big debates in American dialectology has been the role of the "Midlands" dialect: People draw that area differently on maps, but it's generally a narrow band running through the lower Midwest, covering a lot of Ohio, Indiana, Illinois. The question is whether it's a mere 'transitional area' between North and South (Davis & Houck in American Speech and various others have argued this) or a 'real' dialect unto itself (Dennis Preston and others hold this position). The quote in the subject line seems to assume (uncritically, I imagine) the transitional area view: I'm guessing that he's figuring that Ohio, classic whitebread Midwest, doesn't really have much of an accent, and if you have one, it's because you lean toward the North or the South.
In fact, northern Ohio (Cleveland, etc.) is Northern and southeastern Ohio is Southern. As usual, state borders don't match dialect boundaries. These traditional views are based on production – how people talk – rather than how people perceive dialects (either 'perceive' as in how they think they sound when they hear them or how they imagine them to be). Erica Benson of UW-Eau Claire, a key member of the Wisconsin Englishes Project, actually explored how Ohio fits in production and perception in a nice 2003 article: "Folk linguistic perceptions and the mapping of dialect boundaries." American Speech 78.307-330. (She's done a lot of work on constructions like the car needs washed and gas is expensive anymore, features pretty characteristic of the Midlands.)
The map above is her summary map, showing how Ohio dialects look if you consider both production and perception. In part of her perceptual work in Ohio, she gave people maps of the state/region and asked them to identify where people speak distinctively. A lot of people described southeastern Ohio as speaking "hillbilly". It's quite possible that the captain they were quoting is from that area. In that case, it wasn't his "Ohio accent" per se, but the particular Ohio accent he has.
But there's another angle that might play a role: The kind of dialect in question is closely associated with the military. Here's how John Fought describes the role of r-ful Southern (from here):
Over the past century, it appears, the Rful inland varieties of both Northern and Southern speech have continued to gain population and influence not only within their own primary areas, but also at the expense of the Rless coastal varieties. The changing pattern of economic concentration within the country may be driving this shift. Whatever the reason, the cultural importance of Rful Southern now extends far beyond its old upland geographic base. It has long been the prevailing dialect of the military services (except possibly for the Navy), of NASCAR and other auto sports, and of country music, whose performers are expected to imitate it unless they are native speakers, as is Dolly Parton. Rful Southern is naturally associated with the thriving “Redneck” subculture so expertly lampooned by the comedian Jeff Foxworthy, also a native speaker of Rful Southern. In many parts of the country outside its large home territory, even where it is not the dominant dialect, it is strongly represented. Although it is hard to be sure, it seems that not long ago, Rful Southern overtook Rful Northern as the variety of American English spoken by the greatest number of people.I don't know how long it's been so, but there's definitely something to this. For example, I heard a story recently of a linguist who was on a plane next to a career military guy who had monophthongization of /ai/ (that is, he said something like 'ah' for 'I' and so on). They talk for a while and the linguist asks the guy where he's from. Minnesota, born and bred. So, maybe the native dialect of the soldier in this story was strengthened by his association with the military. (As a captain, we can assume he's been in for a long time and identifies powerfully with the military.)
I still wish we weren't reading stories like this in the newspaper.