In other words, is it possible to pool mine in a transparent way?
Yes. A pool operator gives its miners the hash of a block it created in the hopes that some miner will discover a unique solution to a hashing algorithm. If a miner finds a solution it gives it to the pool, and the pool then submits the entire block it created on the network. All the miners know the block hash and can thus verify if it is an accepted block.
In theory, the aggregate set of miners can know when the find a block, because they know the difficulty of a share they found, and can compare to the difficulty required to mine next block. They also have the block hash and can check whether it is present in the blockchain.
However, a single miner cannot know whether another miner on the same pool did find a block, unless that miner or the pool broadcasts that fact.