From pages 7-8 of Crosby's 1979 book "Quality is Free":
"The first struggle, and it is never over, is to overcome the 'conventional wisdom' regarding quality. In some mysterious way each new manager becomes imbued with this conventional wisdom. It says that quality means goodness; that it is unmeasurable; that error is inevitable...and that people just don't give a damn about doing good work. No matter what company they work for, or where they went to school, or where they were raised - they all believe something erroneous like this. But in real life, quality is something quite different. Quality is conformance to requirements; it is precisely measurable; error is not required to fulfill the laws on nature; and people work just as hard now as they ever did. ... What should be obvious from the outset is that people perform to the standards of their leaders."
So Crosby's point is that the term "Quality" is a name for the relationship between two states of affairs: A desired state (The Requirements) and a measured state.(Conforms or does not conform).
Consider the assertion "quality must lie at the heart of all that the NHS does". This is in the first paragraph of the letter sent by Sir David Nicholson to many NHS managers on 24 February 2010 in the wake of the Robert Francis QC Mid-Staffs Inquiry Report (A report about why many hospital patients died unnecessarily).
So do you think that Sir David meant "conformance to requirements must lie at the heart of all that the NHS does" ? Well, his letter talks about many things including "failings",
"scrutiny" and an undefined something called "quality of care". So it seems to me that Sir David's letter uses the term "quality" in accordance with its "conventional wisdom" meaning.
Non sequitur. If you don't state your requirements, you can't measure your quality. That's different from not having quality, or not having requirements. The whole point of Crosby's dictum is that different situations have different requirements, so there can be no single standard set of requirements for data quality.
Following Crosby's philosophy your words "Not having quality" expand into "Not having conformance to requirements". So as I implied, Quality = f(requirements) and so No requirements (expressed using measurable metrics) = No quality.
Now you mention the DMBOK. As I have previously told you, I have not read this book but that does not mean to say that I don't understand quality. e.g. I was involved IBM's internal quality program in the 1970's and 1980's. Since then I have held several management positions where I followed (and fought over) Crosby's philosophy and given many presentations about data fundamentals You seem to be comparing the words in 25 pages of a book, with the knowledge that I have gained in my 44 years of international experience in the IT world - most of which you don't know about.
Lastly, "Requirements" are about the "What" not about the "How". As I see it, a well specified requirement describes a desired state of affairs that can be measured. It has nothing to say about the methods or procedures that may be devised and used to conform to the requirement.
Thus, in Crosby's philosophy, "quality" is a property of the methods that are used to conform to requirements. And, the possibility of devising appropriate methods is directly related to the way in which the requirements are expressed. If your requirements make careful use of metrics then you are on the right track. If you use ambiguous prose then you don't have a hope. (In this regard, I'll read the DMBOK and let you know what I find.)