Try to think it through.
First of all, they cannot increase the latency of their software; in fact, as is explained in the presentation, they work hard to keep it as low as possible and to continue to lower it. An extra layer which must monitor everything would increase latency.
Secondly, what are the algorithms used for determining sanity for this monitoring software? The same ones used to determine behavior of the original system? Then what is the point of writing the second, monitoring system? If it's different, then one of them is incorrect.
if bank_account < 0.9 * prev_bank_account: stop_trading()
What does this mean? As a demonstration of generalization, you might as well have written "if (should_stop) stop;" and similarly affected the discussion.
It's fairly easy to write software that has an 90% probability of being correct. It's maybe three times harder to write software that has a 99% probability of being correct, so ...
Their software needs to be as close to 100% correct as can be reasoned. The speaker notes that the static type checking in OCaml helps a great deal with both reasoning about specifications (what do I think this should actually do?) and preventing errors. Easy factorization in functional programming style helps break the problems into smaller components with little state, as well.
it's cheaper to write 90% likely to be correct software and then another piece of 90% likely to be correct software that checks it.
Assuming those statements are true and it were possible for two discrete systems to function in that manner, that still leaves you with a large amount of known probability for error.
You should watch the video, I think you will find especially interesting the part where he describes how they were unable to pay enough money to get people to even carefully review certain types of code.
Additionally, I think you may be conflating static checking (which OCaml does) with live monitoring of a working system:
Same reason it makes sense to have proof checking software like Metamath.
That is a static check. Metamath does not fork a process and monitor your proof, assuming that were somehow possible.
That's what my intuition says.
Intuition is often correct when dealing with things which are intuitive.