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Can you show us some screen shots? I just embedded a file with the Edit->Attach File command while in project mode, flipped over to context mode, clicked on the paperclip icon and saw my attachment. I then synced, went to another machine and synced, and when I viewed that action on the second machine, the file was there.

Are you absolutely sure you didn't link to the file? Then only the link to the file would be synced, and trying to access the attached file usually would fail.