I don't use (no longer use) Dropbox. 1Password database is synced to my phone via Wi-Fi, and I always have my phone with me so it never really a problem. If I ever leave my phone elsewhere, then I've got a bigger problem anyway.
Dropbox Web UI is just a HTML implementation of 1Password (read-only) sitting in your disk, so its HTTP security depends onto Dropbox (or whatever sync service you use) rather than 1Password itself.
Dropbox Web UI is just a HTML implementation of 1Password (read-only) sitting in your disk, so its HTTP security depends onto Dropbox (or whatever sync service you use) rather than 1Password itself.