Is there anyone making that claim? Apart from straw-men?
As an example, I was once refactoring a Java system. The compiler was happy after about a day, the unit tests after three days.
So if you claim your type system is going to keep your refactoring safe, I'd say that I'm not the one being delusional.
And of course unit tests also tend to, in practice, catch the errors that are caught by types. If you check that a value is equal to 10 rather than 9, you've also implicitly checked that it is not of type PinkElephant.
Now I perfectly understand the feeling that people who are used to the safety-net that static typing appears to give have when encountering a code-base without types. I have the same feeling when encountering a code-base without reasonably comprehensive unit tests (that fail when I poke into the code-base).
The feeling is absolute terror.
I just contend, with reasonably good justification, that this feeling is not particularly justified in the case of static types, because the evidence is just not there.
I haven't checked what the evidentiary status is for unit tests. But then again, I don't make these sorts of categorical claims for unit tests. I just make claims for my experience with unit tests.