That's a bad test though. Its not brittle but assuming it was written in a Tdd manner there should be at least two chances for the developer to catch the bug if they don't use the constant they are testing in the test.
I have no source on this but isn't it bad practice to use constants in your tests? I personally use a new string with the expected value. It forces me to look twice and really consider what I am doing.
But a developer will (should!) find the error immediately.