Haskell is better than most languages at achieving this but still far from the truth. Type systems help a lot but they can't help you in every way. I write Haskell commercially and I can tell you there are many times our test suite catches an issue not caught by the compiler. (In fact just today we have this bug in which a particular maximum function returns the maximum of all historical values of a particular time-varying quantity but forgot to include the current value. The test suite not the compiler found the bug.) But it's also true that with Haskell you can have a smaller and less extensive test suite to maintain the same level of confidence about your code.

Another thing is, if you want to write high reliability code in a general-purpose language, you have to have the discipline not to use all language features because a general-purpose language is by default not safe enough. This article basically outlines a subset of the C language for writing high reliability software, and I imagine if Haskell is used for similar software, a large number of language features and functions in the base library would need to be banned.