Final Cut Pro: Media-Managed projects with .stap files may not open on other computers

Issue or symptom
If you use the Send To Soundtrack feature in Final Cut Pro to create a .stap file (Soundtrack Pro Audio File Project) in a sequence, and that sequence is then copied using Media Manager, the resulting project may not open if it is moved to another computer.
If you try to open such a project on another computer, the project may not open and you may see this message:
Searching for movie data in file "filename".
Products affected
? Final Cut Pro
? Soundtrack Pro
This document will be updated as more information becomes available.