This issue is really odd and I am not aware of reasons for such behavior. My best guess at this point is some incorrect caching that could, potentially, be caused by some proxy, or requests being blocked by a firewall or other similar software (on the server, or on the user machine).
What makes it even stranger is that this manifests with Lightweight render mode - it does not use so many background images, so a missing titlebar would mean missing stylesheets, which indicates some issue with the browser cache or with the webresource urls (for the former there isn't much we can do, for the latter you can see if there are broken requests in the dev toolbar and switch to the CDN if the ideas from this article do not help).
On CDN + intranet - it is possible to create a custom provider on an appropriate server in the intranet as described here. The article treats scripts CDN but the approach for the skins CDN is identical.
If there are additional details you can provide in a ticket - you can open one, but with the same set of information I doubt we will be able to provide a much different answer.
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