When you put a file into a Dropbox-synced folder/directory, Dropbox first syncs the file to their cloud storage in AWS. Once that sync is completed, Dropbox starts to sync to other devices. If you want to sync a large file, you must wait for the cloud sync to complete before it will start to copy it to other devices, which could take longer than copying with a flash drive.
I assumed that was the meaning behind the statement you selected.
I think it has to complete the cloud sync first before it syncs across the local network. It will take advantage of the LAN, but not as immediately as you'd like.
I assumed that was the meaning behind the statement you selected.