According to AOLNEWS:
UFOs have monitored and possibly tampered with American nuclear weapons, according to a group of former Air Force officers who will make their claims public next week at a Washington, D.C., news conference.
Ignore the headlines. Unidentified doesn't automatically mean extraterrestrial. It means exactly what it says; a flying object yet to be identified. Could be a meteor shard. Could be a weather balloon. Could be an unidentified aircraft from a foreign--yet still earth-based--land. Popular usage has confused the term UFO so much the conversation can't help but veer into paranormal territory.
Think of it this way: John Does aren't automatically identified either. Doesn't mean they're from the 5th dimension.
I'm guessing many of these UFOs were foreign spy planes, and yes, it would make perfect sense for foreign spy planes to monitor US nuclear facilities, considering such activities are the very reason spy planes are built in the first place.
As for the US military not going public with the information...not the biggest surprise I've heard today. OF COURSE the government wouldn't go public with real-time info. about their nuclear facilities being compromised. And NATURALLY they'd be even less likely to do so if they couldn't readily identify the crafts in question (particularly if said UFOs were suspected of being Soviet), as it would be a public admission of the vulnerability and perhaps inferiority of US anti-spy technology.
Back then, the US had a credible superpower to scare the rubes with. They didn't need to justify the defense budget using pulp fiction motifs about machete-wielding Bedouins half a globe away.