You’re lucky to have met them.
And BTW, that secretary must have been a prophet. At the time she told you that, Armstrong wasn’t planned to be the first to set foot on the moon. IIRC, it was supposed to be Collins on a different mission. But the Apollo 1 disaster rearranged the schedules.
The initial Apollo flight schedule had Apollo 11 doing essentially what Apollo 10 did, orbit the moon and test out the LM in lunar orbit, do a lunar orbit rendezvous with the CM/SM, and simulate a landing abort by separating the LM landing and ascent stages while in orbit on the "low pass" near the surface. The schedule was bumped up to Apollo 11 making the lunar landing because the LM was not available on schedule to do the original flight plan, which had an additional flight in Earth orbit slated to test the LM at higher altitudes in Earth orbit. That would have made the first landing attempt Apollo 12, and so Pete Conrad might very well have been the First Man. But the schedule was rearranged to cover for the lack of a LM to test earlier on in the schedule. They pushed the Apollo lunar orbit flight back to Apollo 8, which flew without the unavailable LM, and made Apollo 9 the first test of the LM in Earth orbit. That cleared the way for Apollo 10 to be the LM test in lunar orbit, and Apollo 11 as the first landing attempt.
But that is what she said and it came true. In fact,when she said, "you just met the first man to walk on the moon," we asked which one... Elliot See was with him that day. He was later killed.
It was a fun interesting time to be living in Houston. John Glenn was the one I was around the most.