Kawarma: Only dropbox instances which have shared folders use LANSync, and only for those shared folders. Dropbox will never get data from peers you don't share that data with, since that would reveal which data you have or are looking for. Also all LANSync data is encrypted and readable only by the peers that participate in that specific share.
I agree there's some remaining sidechannel potential - e.g. putting something into a share you have with another user that is on the same lan, to test if that user has this file in another share. If they don't, you would expect them to download from you - unless yet someone else on the same lan has the data too. This is true btw, even if you don't use lansync: a new file would trigger a download from our servers and you could analyze network packet data (despite the strong encryption) to see if this is what is happening. Sidechannel attacks like this are hard to deal with, because they require code to handle all cases exactly the same way - which is at odds with doing the case differentiation in the first place and would lead to huge inefficiencies.
We most likely won't be able to deal with all of these corner-cases in the most paranoid way, since, for example, redownloading huge chunks of data that you already have is not behavior that is attractive to a majority of our users. We'll offer you an option to disable LANSync, should you need to do so, but from our own analysis of the security model we think LANsync is solid.