I prefer "responsibility"; "ownership" is, IMO, misapplied here. (Though, arguably, one of the reasons people do not take responsibility is because they don't, in fact, have ownership -- but ownership is a material relationship, and responsibility is the relevant attitude.)
But I think in substance we generally agree.
We do, I think the difference is that my experience has been fixing projects starting from a technical complaint to an outside organization and helping those in an IT/Technology organization drive changes up thru their organization, often into the CEO space when needed. From your choice of wording, I suspect, your experience in this might start higher up the product chain.
Until you have staff, from the CEO down, that own problems, from the mess in the coffee room to server down time, you will have a "business house of cards" no matter how good the process. In fact, most of the time, fixing things involves re-writing and/or reconsidering process - usually starting with asking the question - "Do we really need that?"
You kind of contradict yourself there: if fixing things usually requires changing the process, then "how good the process" is obviously has fairly direct bearing on success. The key thing is that processes aren't good (or bad) in a vacuum, they are good or bad based on the effects they have in your organization, in acheiving your mission; the same nominal process that is good for a group of people when considered against one mission is going to be bad for the same group of people when considered against different goals, and the same process that is good for one group of people with a given mission will suck for another group of people with the same mission, because people matter.
I probably expressed that poorly. To put it another, hopefully more correct way - For organizations you can help (there are plenty that are unreceptive to this kind of help) you have to have to start with the culture. Identify those who have true involvement, are willing to risk take, have decision power... and get all of them committed before you can fix the process, which then finally lets you help fix the bugs/tech. Lather, rinse, repeat till organization functions.
In particularly ill organizations, there is no way to separate these items (or the combatant parties