I'm remembering an Asimov that has robots who can't kill but can allow harm to come to humans. They end up putting humans into deadly situation at Time A, as they know that they are able to save them and so the threat does not apply. And then at Time B not bothering to save them after all.
You are thinking of the short story Little Lost Robot, in which a character (robo-psychologist Susan Calvin) speculated that a robot built with a weakened first law (omitting "or through inaction, allow a human to come to harm") may harm a human in that way, though it never occurs in the story.
Many people think you can solve the Friendly AI problem just by writing certain failsafe rules into the superintelligent machine's programming, like Asimov's Three Laws of Robotics. I thought the rebuttal to this was in "Basic AI Drives" or one of Yudkowsky's major articles, but after skimming them, I haven't found it. Where are the arguments concerning this suggestion?