Fremont is off limits due to some very rare vegetation. It only grows here. It is not found on the other San Francisco Peaks. Climbing is off limits during Summer, but is a relatively easy Winter climb, when the crown is covered with snow. Chances of being caught by a ranger are remote but do exist. Local Indian tribes do consider this area sacred, and if caught on the peak could cause you more trouble than a ranger.
What I've heard and read contradicts what chubb says.
The vegetation is seneca franciscanus, and it grows not only on Fremont Peak but on all the San Fransisco Peaks. However, it only grows above treeline (~11,500 feet plus or minus 100 or so). This is why you're not allowed to climb Agassiz unless it's snow-covered. Humphreys Peak is permitted because there's long been an established trail to the top, but there are not trails to Agassiz and Fremont, which is why they're off-limits.