If the bugs are that subtle what makes you think you're unit tests are comprehensive enough to catch them? The hardest bugs to debug are the types that show only on high latency networks and only when dealing with files bigger than 2GB and only after the app has been running for at least 50 hours. Those are also the type of bugs which are almost impossible to write unit tests for.
I'm not arguing against unit tests, they definitely have a time and a place. I'm just not convinced that they are an easy and instant cure for all your hardest bugs.
Unit tests may leave you with remaining subtle bugs. This is better than having both subtle and obvious bugs. Obvious under test, e.g. "the class returns null when it should return object y", which can have subtle and easy-to-miss symptoms in a production system
I'm not arguing against unit tests, they definitely have a time and a place. I'm just not convinced that they are an easy and instant cure for all your hardest bugs.