The solidity documentation says that
Everything that is inside a contract is visible to all external observers. Making something private only prevents other contracts from accessing and modifying the information, but it will still be visible to the whole world outside of the blockchain.
What does this boil down to? Of course that the node running code involving a private member knows its type and value and that given the contract address you could get this info as well. But is there anything more to this transparency? I guess that in order to find anything else about the private member you would have to do some serious reverse engineering (assuming that you do not have an ABI).