Haskell does not practically eliminate the need for tests. I am very concerned that Haskell programmers are getting the reputation for claiming such things because they're simply not true.

Haskell's type system does statically check many things you might want to write tests for which makes those particular tests unnecessary, but it doesn't eliminate the need for tests in general. If you hear any Haskell programmers making claims that sound like that please ask them to be more precise.