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A common problem is the use of page-relative on-page links ( e.g. <img src="image.gif"> as opposed to <img src="/image.gif"> ) combined with a failure to recognize and rewrite those links in the logic used to map subdomains to (sub)directories. Therefore, it's possible that the image requests in this case are being resolved to an improper filepath, and that that filespace is off-limits to HTTP requests.
The problem isn't anywhere as complicated as it sounds; This description is generalized and based on incomplete knowledge of the problem, and as such, can't be mcuh more specific or be put much more simply. The error log will likely be quite helpful in focusing the investigation.
Log into your site using FTP, and try navigating UP from your top-level domain. If you can get to other people's sites by doing that, then it's time to find a new host. Otherwise, you're just hacker-bait...
Back to your original question, you might want to check to see if you have anti-hotlinking code in your .htaccess file, or "hotlinking protection" enabled in your control panel. It may be that for the "site" where the image exists, the other site is considered an "external site" and therefore is not allowed to refer the image request.