Not counting their initial failures, SpaceX has had a 100% success rate. And each rocket was so significantly different from the previous rocket[1], that it's more fair to say they had 3 rocket models with 100% failure, rather than one model with 60% failure rate. And the Falcon 9 has a 100% success rate. And they were awarded this contract, so obviously NASA believes they can achieve the desired reliability and safety for the rocket that will be used under the contract (
not F1).
I'm not affiliated with SpaceX, nor trying to be a fanboi, but I believe you are distorting things.
[1] Which did earn them a lot of criticism from the industry, actually