Your packing lists are stored in your own Google Drive and synced to every device you sign in on. Nothing is shared unless you choose to share it.
Open any template or trip and tap the Share button in its header to give someone else access to just that list. Lists shared with you appear under Shared with me in the tab bar.
Shared with me
Did someone share a list with you? Pick it from your Google Drive to add it to your Shared with me tabs.