It's not slow to test a rails app. See DHH's latest post.
But due to the high degree of coupling of logic to AR model code, callbacks, etc., you end up testing much of Rails along with your own logic, which makes the tests slow.
If your "business logic" is just Rails associations and one or two callbacks, then arguably (and this is what DHH is arguing, I think) it probably doesn't need to be unit tested. Other parts of your app are far more likely to break or behave unexpectedly.
However if you are doing any kind of nontrivial software design, unit tests + TDD can be extremely helpful.