Can my doctoral adviser take my dissertation and publish it without me?
I think there's a disconnect between what the assistant chair means when they say "take responsibility for finishing and publishing the papers" and what you're interpreting it to mean.

What I imagine they mean is that your advisor would have to do all the editing to get the results into a publishable format, tying up loose ends of experiments, submitting the paper to the journal, etc. -- coordinating the myriad things needed to get a body of work into a publishable form. I don't think she's talking about taking the paper, removing your name from the author list and submitting it behind your back. -- You'd likely be informed about the submission, even if it's merely at the level of your advisor emailing "here's the finished manuscript, any comments before we submit?".

You're absolutely correct that you, as author and a person who did the work, have a say in whether something gets published. And you're also correct in saying that it's unethical for your advisor to ignore you and publish without your consent (either with or without your name on the author list). However, it'd also be unethical for you to hold up publication of an article for non-scientific reasons [1]. As such, it's normally expected that any research work you do is probably going to get published, and if you don't do it yourself someone else is going to do the legwork to make it happen. (Giving you the appropriate credit [2].)

So it's all about how much "with[out] me" you're thinking about. Once the results are done, coauthors can have very, very little to do with the actual publishing of the paper. Other authors can do all the work of collating the results, analyzing them, writing, formatting, etc., and the coauthor can just look at the manuscript and say "Yup, looks okay to me!" and that counts as permission to publish. 



[1] If you have scientific objections to the article as written, that's one thing - work with your advisor to address them. But if you think the article is scientifically sound but disagree with publication because you no longer care about it, or you want to hurt your advisor, etc., that's another.

[2] "Appropriate credit" drops off the less involvement you have in writing the paper. In certain circumstances, not actually writing the paper could knock you off of "first author" status. (For those fields which order authors by contribution amounts.)