In order for a database to provide such guarantees it needs some guarantees from an underlying hardware.

Mainly that when disk say that data was written, it really was written, and that the data was written in the right order.

The danger with overlay systems is that they might not provide these guarantees, which makes database writes unsafe. Given that current overlay drivers are unstable as it is, I doubt they put any effort to enforce such guarantees.

Not exactly a database but for example with ZFS it is known that ZFS can't provide guarantees that usually provides if you run it in a VM, unless you have a hardware that supports VT-d (a.k.a. PCI pass-through) and have it enabled.