Sorry; I assumed you weren't keeping private info in your directory names (seriously, is this a discussion of your actual requirements, or just an exhaustive exploration of a DreamHost claim?). You can certainly deny others from getting a directory listing or seeing your file structure -- that's what the "executable" permission on directories is for (reread my notes on umask settings above... umask 077 is what you want). I just suggested leaving that alone because it's easy to cause yourself problems if you forget which folder is set how... and for "other" (like Apache) to access anything in a given folder, it needs 'x' access to all parent folders. It's like most computer security; you trade off convenience for security.
Meaning that other users on the same server can associate your username with your website? And figure out that you run sites X, Y & Z? Well, this is likewise avoidable; for site superduper.com, create the user superduper, put them in group superduper, and give the site to that user. Repeat with other sites. Don't forget you're legally required to use accurate info in your domain registration -- that's probably an easier way to link your sites, if someone wants to.
But more importantly -- if this is a serious concern, you are not a good candidate for shared hosting. Get a VPS or dedicated server somewhere. The Dreamhost servers are quite secure compared to many other shared hosting solutions -- there are plenty of hosts where you can't run PHP as CGI without a special request... which means that almost everyone has plenty of files that anybody on the server can write. Is that dangerous? Not really, if you're just hosting baby pics and a blog. Another user doesn't want to lose their own hosting and possibly face legal trouble just to photoshop a funny face on your baby. But if you're hosting sensitive data, and operating sensitive sites on shared hosting, you're in the wrong place.... Partly just because if you get your permissions wrong, your sensitive data is readable by strangers.