I get the idea that it's pretty certain that he actually couldn't, but at that time I don't think you could be certain of anything he might be able to do.
Maybe not set of nuclear missiles, but destroying evidence perhaps? Or some other scheme that would only require a simple digital initiation?
As I'm sure you are well aware there actually were hackers at the time who taught themselves to whistle at 2600hz. Who knows if someone you have just caught and otherwise know nothing about could do something similar?