You are correct.
OC don't usually get the free reign to do what they want like DC's do. That is to say, a HC (defensive or offensive-minded) is more likely to allow a DC to come in & turn him completely loose to let him run his own type of defense how he wants. OC's however almost never get that free reign to install and run what they might be partial to. If its an offensive-minded HC, they will typically be calling the plays themselves & the OC is really just there in name only. If it's a defensive-minded HC, its can happen, its just much more rare. The typical set up for those guys is to have their OC's run ball/clock control type of offenses to protect their defenses. On the rare occasion an OC is given free reign, the person turned loose has to be an established mind...Think Kubiak to Minny under Zimmer...Norv Turner to SD under Phillips.
I say all that to say that i don't think we've seen Schottenheimer really spread his wings b/c he's always been under defensive-minded guys. Still though his last name might be enough to scare people away for fear of "marty-ball" having rubbed off on him.
me personally, i think i'm partial to a defensive guy. We've failed with both & actually we have failed more with offensive minded HC's now than defensive. That's why i'm weary of hiring "the next great offensive genius/mind"...whatever. You're only as much of a genius as the offensive talent you have says you are. CAN YOU BUILD AN OFFENSIVE BASE OF TALENT TO EXECUTE YOUR VISION? That's what fans should be asking instead of looking at the success the guy had working under another successful guy. & i don't have any data to prove this, but it is my impression that offensive..or offensive-linked guys flame out much faster than defensive aligned guys, usually b/c those guys can't get enough of that base level of talent they need to be successful..