They haven't denied it yet because they have to ask his son, who is not involved with the campaign, what happened. They probably want to get all their facts straight before denying anything.
They would have done this immediately upon seeing the story; checking the veracity of a single highly significant fact which purports to originate from a known source doesn't take a week. Anything more than a half-day delay in responding is significant; they could have produced a repudiation video by now.
This doesn't necessarily mean that the story is true, just that the campaign has made a deliberate choice.
This doesn't necessarily mean that the story is true, just that the campaign has made a deliberate choice.