I've demonstrated that Biden did not make any arithmetic errors, at least not those presented as such in the various articles tearing her dissertation apart. She's got a couple typos, that's all you've got. I've also demonstrated that typos can occur in publications that have clearly been proofread, so it's completely disingenuous to suggest she didn't proofread just because a couple typos slipped through. Finally, I've demonstrated that the EdD program at the University of Delaware is substantively similar to other doctorates.
The AP's guidelines are devised by a news organization to ensure that the writing style is clear to a general public that is not well-versed in the world of academia. In that context, it is perfectly understandable, but it does not say anything about how one should refer to someone within their own professional context. One is for clarity of communication, one is for professional etiquette. I've not noticed, outside of the the context of the controversy itself or when speaking specifically of her education, that the media has used the title when referring to her. She uses it on her Twitter handle, which is, admittedly, outside of the professional context; but hell, she's allowed to be proud of her accomplishments, and she's far from the only person who does it. There's also the job title issue to consider. If someone asked me what an MD's job was, I'd say "they're a doctor." If someone asked me what a PhD's (or other degree-holder who works in higher ed) job was, I'd say "they're a professor." So, in news writing, it's appropriate to establish the credentials of the person by saying "Professor of _____ Studies at the University of ______." It's simply a quirk of the language that someone can be a doctor by profession but can also be a doctor by credential. So, I see no problem with news writing adopting this policy for the sake of clarity.
Suggesting she should be the surgeon general is dumb, and shows a lack of knowledge of what her credentials actually are. That demonstrates an error by that particular host, nothing more. That does not mean Biden's credentials are not valid for what they purport to be.
Given your unwillingness to accept the problems with the criticism of her culminating document, which are demonstrably false, I can see we're not getting anywhere. As the weekend nears its end, I've got plenty of work to do, so this is where we'll just have to agree to disagree. I'll suggest that no one had a problem with using the term "doctor" to refer to those with all kinds of doctorates (in the appropriate context, of course) until a First Lady who plays for the blue team had the audacity to be highly educated.