Answering your question specifically would involve too much speculation, so I'll try to address the broader historical possibilities. We have a few possible scenarios here:
- Your gentleman could be telling the truth. If the details of the mission remain classified, not only should he not have told you, but there would be no way for historians to interrogate his account and deliver a verdict. We couldn't answer you (and some who could, classified history is a discipline, wouldn't). If such a mission happened and has been unclassified, you would think that this would appear in the historical record. Maybe not at a high school level, but it would be a significant Cold War event. Someone more knowledgeable than I may come along and correct me, but I don't see this as likely.
- He could be mis-remembering and/or exaggerating certain details for effect or due to the vagaries of memory. This is a danger with primary sources/anecdotes. Operation Chrome Dome was regular flights of nuclear armed strategic bombers along the borders of the US as a strategic deterrent during the Cold War.
- He's knowingly relating a false story.