Hello Jim,
I wasn't able to reproduce your problem I'm afraid. I took the
New / Sample Diagrams / Process Improvement cross-functional flowchart, used
Home / Editing / Select / Select by type / Layer (see attached image below), hit Ok and Ctrl + C to get my selection. I then pasted into a new blank document and only the expected shapes came across (ie, none of the containers). Does this work for you if use the same sample diagram?
Although I believe this particular scenario works correctly, you might also be interested in David Parker's multiSelect addin, which allows you to create selections based on master type, relationships to another shape and categories:
http://blog.bvisual.net/2012/07/20/multiple-selection-methods-for-visio-diagrams/Let me know if this works on the sample diagram and then we can investigate what's going on with your specific document.
Hope that helps.
Best regards
John