... I still don't fully see the connection. Is it that PoW makes one version of a blockchain more credible because someone invested the work? That kinda makes sense, what my ex called "the high heels proof". While I get the immediate notion of that, it seems like a leap to make one equal the other?
It's more like a game theory in a sense. To reverse a transaction that is included in a block within a blockchain that is X blocks deep, an attacker has to build another blockchain from the block before that and include another transaction that is spending the same coins but is sent to another address instead. Now, since nodes only accept the blockchain with the largest PoW, the attacker has to effectively outpace the rest of the network and be able to mine X + 1 block. Remember that the rest of the network is also mining at the same time and lengthening the blockchain. As such, it is both prohibitively expensive as well as unprofitable to do so.
Consensus is an important aspect with any distributed systems. The concept is difficult to explain if you don't understand the workings of Bitcoin. It'll be great if you could skim through the whitepaper and clarify if you don't understand anything.
https://bitcoin.org/bitcoin.pdf