This is actually a pretty common occurrence, and is caused by the CMS's re-write rules interfering with the navigation to the subdir.
You didn't share which CMS you are using, so I can't respond with complete detail, but the fix for this situation is actually very simple. The DreamHost wiki has an article on this called Making stats available with .htaccess" which describes how to modify your .htaccess file to allow the stats dir to be served in this situation.
The article uses a WordPress installation for it's example, but the process is very much the same with other CMS systems. There are some other specific examples also in the wiki (see http://wiki.dreamhost.com/Mod_rewrite#Problem_with_.2Fstats).
Even if your CMS is not shown in a specific example, if you study the examples that are available, you should be able to figure out what you need to do in your circumstance.
The subdomain pointing to the stats dir isn't going to work (as you discovered), so you will need to tweak your CMS .htaccess as indicated in the above paragraphs to let the stats dir "slip through" the re-writes.