IMHO untested code isn't always a bad thing. Anything related to privacy, security, or data integrity should be heavily tested.
But beyond that, code should need to earn its tests. (At least in a web startup context.) After all, the core of agility is being able and willing to go in a different direction when something isn't working.
In addition, if you are truly in the earliest stages of your startup (pre-revenue/traction) the tests are not needed -- but you have to be _very_ aware that you are making a tradeoff for sheer velocity and you will have to pay the price later on. I've seen too many startups fail to pay the price and it comes back to haunt them and reduces their overall velocity.
"If your code doesn't have tests then you can't refactor" is pure dogma and trivial to falsify (go on, refactor some untested code now!). More likely to introduce bugs? Perhaps. But relying on that absolutist statement about refactoring will alienate me every time.