But what exactly do you mean by "stake"? For example, if I controlled 51% of the stake in the genesis block, could I take over the network? If the answer is no, then the statement "Bitshares is secure provided 51% of stake is honest" is incomplete.
Any stake older than 101 blocks before the
current block is irrelevant in bitshares, just as any work performed prior to 6 blocks before the current block is irrelevant in bitcoin, as a general guideline.
When I asked you to define exactly what you mean by "stake," the definition you gave included a new term: "the current block."
But how do you come to consensus on what is the "current block"? Since producing PoS blocks is not costly like PoW, if I control 51% of the stake in the genesis block, I can create a new transaction history just as long/complex as yours, with a new--and different--current block. So again, the statement "Bitshares is secure provided 51% of stake is honest" is incomplete because you haven't defined what stake you're talking about. Note that in PoW it's easy to define the current block: it's the block at the tip of the valid chain with the greatest cumulative work.
Andrew's done a good job explaining these subtle issues in the paper cited by Raystonn in the OP.