Safety can mean many things. I'm fairly sure JVM will keep the C-level memory safety guarantee after an OOM, but you can still end up with Java objects in inconsistent states that will start throwing exceptions when you poke them.

The reason why these exceptions are so "unsafe" is that they can occur at any moment. Maybe you were in the middle of modifying some data structure which will enter an infinite loop the next time you touch it. It's a bit like signals in C where you have to be extremely careful about the APIs you use, except worse because exceptions unwind the stack. At least in C you can still safely call kernel syscalls regardless of userspace state.