Then let me clarify the comment. By offensive-minded, I mean a guy that knows offense, that understands it, a guy that has coached it. To cite Tony Dungy as a counter-example is inane. When Dungy was hired, he was hired with a mandate not to mess with the offense. It was already in place. Tom Moore was the OC in Indy before Dungy got there. All of the prominent players on offense were already there. A better example would be Dungy's offenses in Tampa, which were consistently terrible (5 out of 6-years they ranked in the bottom half of the league.) Seifert is another horrible example, since he was promoted from within and inherited players and a system from his predecessor. Marvin Lewis inherited his offense too. Bob Bratkowski was the OC two years before Lewis got there. Palmer was drafted the year Lewis arrived. Houshmanzadeh, Chad Johnson, Rudi Johnson, Willie Anderson, Levi Jones, etc. predated Lewis.
Nick Saban, Dave Wannstadt, and Jimmy Johnson were defensive coaches and we see what wonders they did with the Dolphins offense. The Bears offense is terrible, so if the Cover Two defense (his forte) and its inherent weaknesses don't scare you away from Rivera, his lack of exposure to anything resembling a decent offense should.