I suspect, from your question, that you're saving these resources on a shared directory of some sort? A workgroup server or something similar?
If so, your problem is most likely coming from the differences in path names inherent in the two platforms. PCs and Macs use different conventions for path names, so, if the reference is stored by a Mac, then it'll be meaningless to a PC, and vice versa.
You have a few options:
1) You can manually store the files in the server resource and then calculate a URL that works on each platform. Store that on the record and use Open URL to open the resource. This works if you have an individual who can control the workgroup contents and path names. Doesn't work so well if you want to allow a wide range of users to insert the resources (unless you train them to capture the path names in the URL field).
2) If you're using FileMaker 12, store the files in the database and turn on External Storage. This will cause FileMaker to store the resources in a directory tree of its own creation, accessible from either platform.
3) If you're on version 11 or earlier, have a look at SuperContainer from 360Works (www.360works.com). It's a server-side utility that causes a web viewer to act like, well, a super container field. :-)
4) Last, and least, store the resources inside the database (version 11 or earlier), which, as you said, isn't ideal.
There is a chance that it has nothing to do with FileMaker.
It could be an issue of "ownership" when the user saves the work they become the owner if they don't expressly change that in Properties / Get Info.
The problem probably is that your container field is storing a reference to a file, which is stored on a share in your network. If a user inserts a file on the Windows platform a file reference with the 'filewin://' prefix is stored. On Windows, the FileMaker Pro client can resolve the file path pointing to the file, and FileMaker shows an appropriate icon in the container field. File references in container on the Mac OS platform expect a 'filemac://' prefix. All about file paths in FileMaker here: http://www.filemaker.com/help/html/create_db.8.32.html#1030283
The workaround would be a script attached to a button, which dynamically constructs the file path depending on the OS the user is on (use Get(SystemPlatform)!).