I'm going to assume you're in a situation where you can add additional web parts to the page and not trying to add JavaScript to the DataView Web Part directly. My suggestion won't work on a separate page if a Designer adds another view of this list.
Upload a blank .js file to your Site Assets. Add a Content Editor Web Part to your page, point it at that file. Add JQuery from a provider or host it yourself, adding the reference in your file. From there, you have 3 directions in which to work: first, explore the web part with Internet Explorer's F12 Developer Tools, keeping a particular eye on divs and tables with good unique ids, names, or classes that would solve your problem if hidden. Also keep an eye on the id of the div or table or cell or whatever that contains your access denied text. Second, (assuming you're new to JQuery) do some JQuery tutorials and then start playing with selecting the above items and, say, changing their background color. Once you have both of those, you're 90% there: (try to) select the object that would contain the access denied text, and if the innerHTML is present and equals that string, then set display:none for the div or tables to hide your web part. The third tool you have is editing the page directly with SharePoint Designer: you can toss a div with an id of your choosing around any xsl:template, which might help in your JQuery selecting.
I'm sorry I can't give you the specific code, since I'm not in a position to test it. If that changes, I'll try and give a more detailed response.
Old, misdirected answer: Do either of the answers here work for you? Alternatively, this answer has some great resources to solve your problem. Just change the message to an empty string.