Just as the resort CM's have great latitude in issuing UPH's, the Guest Relations CM's have great latitude in renewing AP/PAP's. If you get the right one you can even get a renewal months after it first expired. It will of course be backdated but it *can* still be done.
You won't find any GR CM's who will decline to renew your pass within 30 days past the date. After that time frame, it depends on who you get. It's all up to them.
Disney's policies, even those in writing like the AP renewal, aren't always the practices that are applied in those situations. Think of the "must have valid AP at check-in" or "UPH's must be purchased for all members of your party", et al.
By the way, the DU quote is worded incorrectly even by Disney's standards. It should say: "You must renew on or before your expiration date, and your pass will be valid for one year from the original expiration date, not the date of first use." The date of the renewal has nothing to do with it. It's the date of expiration on the original pass that counts.