As the problem becomes complex, you can't remember all the requirements, period.

Exactly, but if I start from working code with a lot of tests I don't need to remember the requirements. I just need to know my current requirement and figure out the ones I'm changing with my new requirement. It doesn't catch everything, but in most cases if I break some other requirement I find out about it and can figure out just that one more requirement and not the millions of others that still work.