Answer:
The educational standard that is most commonly recognized by large employers and government agencies is that a valid university degree must be granted by an institution that is "Regionally Accredited" by one of the six accrediting bodies that are recognized by the U.S. Department of Education (USDOE).
The University of Phoenix is accredited by The Higher Learning Commission and is a member of the North Central Association (NCA), which is one of the six recognized by the USDOE. This is the same accreditation credential held by all major universities within the NCA's jurisdiction, including the University of Arizona, Arizona State University, the University of Michigan, Ohio State University, Notre Dame, Indiana University, the University of Nebraska, and dozens of others.
Since regional accreditation is what counts in most employers eyes, a degree from the University of Phoenix is recognized as an accredited university degree and is accepted by most, if not all, major employers and government agencies. In fact, having served as adjunct faculty at two state universities, as an administrator in a community college system, and as senior management for a major media company, I can tell you that I have worked with University of Phoenix graduates in all four cases, including tenured faculty members and corporate executives. (Note: I am not a graduate or employee of, or have any relationship whatsoever with the University of Phoenix).
That said, no two hiring managers are the same, just like no two colleges are the same. Specific hiring managers may weigh the value of a non-traditional university degree differently than one from a brick-and-mortar institution, much like the value of a degree from Harvard or Stanford might be weighed differently than a degree from a state university or small private college.