It's the scheme, coaches, players, and Front Office. Under Jimmy Johnson and Bill Parcells, the team put more emphasis on defense than on offense. From 2000 through 2012 they drafted only 3 players at the offensive skill positions (QB, RB, WR, and TE) in the 1st round (Ronnie Brown, Ted Ginn Jr, and Ryan Tannehill). In the first 3 rounds they drafted a total of just 8 or 9 players at these positions. So, they usually had a decent defense, but an average (on a good day) offense. This is why Sparano's team did okay between the 20s but settled for FGs instead of TDS; they needed more talent at the skill positions.
The team already had a half-decent foundation. The defense needed some secondary help but had a Top 5 Rushing Defense. The offense needed to find a RT and replace the injured Jake Long, draft offensive talent, and get better playcalling. A complete housecleaning was in order; they needed a GM who could recognize (and draft) offensive talent, and a coaching staff that could improve what was already in place with better playcalling. Ross made a HUGE mistake by not firing both Sparano AND Ireland, and every personnel decision made by him since then has also been a mistake. Instead of finding a Head Coach who could improve the current team, Ross hired Philbin... a guy with NO experience as a HC, and who was an OC but didn't call the plays. Even worse was the fact that Philbin wanted to change everything about the team, and he sure did! Coyle ditched the 3-4 and the Top 5 Rushing Defense immediately dropped in the rankings. Philbin got rid of talented players and Ireland replaced them with inferior players. Under Philbin, the o-line was gutted. They replaced the overpaid, oft-injured Long with the overpaid, oft-injured Albert at LT. Philbin preferred players like Jonathan Martin and Dallas Thomas over guys like Incognito and Jerry to execute his zone-blocking schemes. The running game was replaced with the short pass, and bye-bye FB position. (I'll bet Philbin wished he had kept Lousaka "Mr. Automatic First Down" Polite!) Philbin wanted a fancy finesse team, not an old-school physically dominating team. Ireland was replaced by Hickey, who was replaced by Tannenbaum. Philbin's team was weak; they were consistently pushed around on both sides of the ball by tough, physical teams.
Philbin (with help from Ireland and Tannenbaum) turned a decent team into a laughingstock, with a roster mostly comprised of of weak, non-blocking, non-tackling, below-average under-achievers running pathetic and ineffective offensive and defensive schemes. At this point, Ross should have done what was needed before; a complete housecleaning. But NOOOOOOOO! Ross promotes Tannenbaum to VP, and they hire Gase as Head Coach (who then hires Joseph as DC). Gase also prefers the same style of short pass offense as Philbin, and the defense under Joseph (another Bengals secondary coach, same as Coyle) is just as bad as Coyle's defense. Joseph takes over as Denver's HC (and their defense takes a nosedive), and Gase promotes Burke (another Bengals coach) so he can continue to run the same ineffective defense. All the while, Tannenbaum and the Front Office continue to fail to do their jobs.
I'm not a huge Tannehill fan, but evidently his mobility hid a lot of defects on this team. Without him, the o-line has shown its true ineptness, the playcalling looks even worse, and the pathetic, ineffective defense is constantly playing from behind. It's a miracle that they won 4 games. If only Ross had done the logical thing and hired people to improve the team that he bought, instead of hiring those who wanted to change everything (for the worse). So yes; the problem lies with the schemes, coaches, players, and Front Office... and the owner!