I think this has now changed. Back in September they changed the way in which Dropbox sync worked, when Dropbox retired their old APIs.
Many people were left with iOS and Android devices that no longer synced. Annoyingly they had launched a new iOS app and removed the old one from the AppStore. Users were left with the only option to 'rebuy' the app again.
Many users were pissed by AgileBits decision to do this. They blamed the Apple policy of not being able to update withdrawn apps, but to most people that smelled of horseshit.
I think that all of their apps now use the new Dropbox API. Old versions of the 1password app on iPad still work, but don't sync. It isn't immediately obvious though until you look to use a new secure note created on the PC and find it missing on the iPad.