It depends on how comprehensive they are, and how important it is that your container operates correctly.

For example, even the best integration tests (for small/mid-size companies) don't always include tests that exercise weird paths around dates/times - leap years, leap seconds, daylight savings time, etc. We often trust that our datetime library or code will handle these for us, but what if the configuration is stored in a file that isn't accessed during your integration tests?

Best case scenario is you hit the error-path soon in production and your code either crashes or does something correct-enough with a fallback path, but a worse scenario is you start losing critical information and don't realize it/fix it until it's gone on for a while.

In a non-trivial app, you can never guarantee that your "good integration tests" cover every edge case. If you could, we wouldn't have outages in production.