According to this post from a Sub veteran, the USS San Francisco's fathometer (sea-bottom detector) would have been running, even if they were cruising in "stealth mode." This would have picked up the decreasing depth as they approached an undersea mountain -- even an uncharted one.

Curiouser and curiouser...

For all the latest scuttlebutt on the San Francisco's mysterious accident, be sure to peruse Rontini's sub-oriented bulletin board. Some of the members are familiar with the vessel and her crew.