“Previously Published Work:

Work by the thesis/dissertation author which is published prior to thesis/dissertation submission (or is shortly expected to be published) may be accepted as part of the thesis/dissertation, provided the committee approves the work and the published material was written specifically to fulfill thesis/dissertation requirements. If you submit previously published copyrighted work and you are not the copyright holder, a letter of permission from the copyright holder must accompany the thesis/dissertation. In no case may work used for a previous degree be submitted.

Your department may permit you to submit multiple-authored work as thesis/dissertation material if you are first author of the work. Your contributions must be clearly and fully indicated in a preface to the thesis/dissertation.”

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The two statements aren’t contradictory. The first statement doesn’t have anything to do with second authors:

The “first author” requirement for T&D is to ensure that submissions that include another author are primarily the work of the thesis/dissertation author. You can only include multiple-authored work (published or not) where you are the first author (only exception I know of is if the norms of the field do not include “first author”). That requirement has nothing to do with copyright and is an academic requirement. You would have to talk to the T&D office as well as your committee chair regarding being able to use those works.

When two or more persons author a work jointly, intending the contributions to meld into an indivisible whole, all the authors own the copyright together. Or the authors may come to an agreement prior to writing to dictate who owns the copyright. Absent an agreement, any of the authors that own the copyright may republish or license the work, except for an exclusive license, which all authors must agree to.

The “previously published work” requirement is both an academic requirement and a copyright matter. You must obtain permission from your committee to republish your previously published work – and this implies that it is a single-author work. If you have assigned the copyright in that work to the publisher, you must obtain the publisher’s permission before including it in the dissertation, and that permission must accompany the dissertation. Unfortunately, most authors don’t understand that when they publish an article and assign the copyright in the article, they may not republish the article, incorporate it, or rewrite it, without the permission of the publisher/copyright holder.

In short, this is what the guide says: you may use your own work in your thesis if it was written as part of your thesis work (this implies single author works). If you aren’t the copyright owner then you need permission. And then they make an exception for multi-author works where the thesis author was the first author.