To slightly oversimplify, it wasn't beyond spec, the spec for the part just wasn't really defined.
The conversation the night before launch went something like this:
Contractor: "We don't want to launch, we're worried about how the cold will affect the O-ring"
NASA: "Do you have any data showing that the O-rings will fail at 50°F?"
Contractor: "No, but we don't have any data showing that they won't fail at 50°F"
NASA: "We launched when it was cold before and nothing went wrong" (The coldest launch before Challenger was successful, although both of the SRBs had badly charred O-rings)
Contractor: "Once, and there is circumstantial evidence that the O-rings had issues on that launch. (managers kicks engineers out of the room). We're not telling you not to launch."
That said, the hardness of the O-rings wasn't the only issue (at least, by itself it may not have caused the Challenger to explode). There was some putty around the O-rings that had problems. It was known to let water in, and the night before the launch it rained and was cold enough that the water that got in next to the O-rings could've frozen and kept them from maintaining their seal. There were primary and secondary O-rings, but the secondary O-rings didn't really give good redundancy.
Contractor: "We don't want to launch, we're worried about how the cold will affect the O-ring"
NASA: "Do you have any data showing that the O-rings will fail at 50°F?"
Contractor: "No, but we don't have any data showing that they won't fail at 50°F"
NASA: "We launched when it was cold before and nothing went wrong" (The coldest launch before Challenger was successful, although both of the SRBs had badly charred O-rings)
Contractor: "Once, and there is circumstantial evidence that the O-rings had issues on that launch. (managers kicks engineers out of the room). We're not telling you not to launch."
That said, the hardness of the O-rings wasn't the only issue (at least, by itself it may not have caused the Challenger to explode). There was some putty around the O-rings that had problems. It was known to let water in, and the night before the launch it rained and was cold enough that the water that got in next to the O-rings could've frozen and kept them from maintaining their seal. There were primary and secondary O-rings, but the secondary O-rings didn't really give good redundancy.