They even have an export function to dump the passwords (unencrypted) into a plain text or CSV file, so you can easily migrate the data to a new manager if needed.
To add to this all syncing on 1Password is done using 3rd party vendors.
You can use dropbox, iCloud, Google Drive, etc to do the actual syncing of the encrypted files.
I can spend $40-80 and buy a bunch of 1Password license packages, or I can use KeePass and place the database in my Dropbox folder. Yes, 1Password has a more aesthetic interface, but otherwise it basically does the exact same thing.
Point being the sync is platform agnostic. The etcetera covers BT Sync.
Just keep a copy on a local computer with Dropbox if need be.
The sync folder is encrypted—is there some risk I'm not seeing?
For you, I would just keep a copy elsewhere (friends computer etc.) or just get an additional device (mobile or otherwise).