And they received $0 worth of assurance that it would be successful. If it were my $150M I would not want to leave it up to the block chain and hope it works.
And even if it won't be mined, the worst case scenario is that you would keep your Bitcoins and can try re-sending them later, they won't disappear to anywhere.
That is the justification Satoshi Naakamoto gave in the original paper for waiting for 6 blocks for a full confirmation.
No they did not. Mathematics is about proofs; Bitcoin does not even have the rigorous definitions needed for that.
To put it another way, what you said is the equivalent of saying that Hacker News gives you mathematical guarantees of security because it happens to use TLS.
That's not how it works, sorry. If you don't double spend your transaction and you attach a proper fee it's going to get in the chain, period.