I am not an expert, I am just learning from what is posted on forums, too.  But basically mining pools have a way to "steal" the hash of newly mined blocks from each other, even before those blocks get out to the relay nodes. They must immediately start to mine a new block Y with the stolen block X as the parent,  without waiting for X to propagate out to the relay nodes, otherwise the pool that mined X will have many seconds of head start.  If they are lucky, they will solve block Y even before the block X has finished propagating to the nodes and the nodes have validated it.

Those miners do validate the transactions that they put into block Y (in parallel with mining it), but they cannot start validating block X, or even check whether it was mined by a v3 miner, because they only have the hash of block X, nothing else.  Apparently they used to fetch and check block X, also in parallel with mining, once it became available; but F2Pool had stopped doing so,  because (they said) it had cost them a block reward once (perhaps by using up some of their internet bandwidth).

Usually this shortcut works, because the block X was verified by its miner, and is valid 99.99% of the time.  Hoever, just after the BIP66 rule became active, the miner BTCNuggets, that was still running v2 software, happened to mine the next block X. The BTC-China pool stole its hash from BTCNuggets, and F2Pool stole it from BTC-China.  F2Pool (who had upgraded to v3) mined a new block Y on top of X, without realizing that X was invalid because it was mined with v2 rules.  Then F2Pool mined another block Z on top of it, and AntPool mined another one on top of Z, and so on -- all without realizing that X was invalid.