Unfortunately, it isn't an urban legend and security hasn't "always been tight."
Warning, sad story follows:
"In June 1973, an 18-year-old man drowned while attempting to swim across the "Rivers of America". He and his 10-year-old brother stayed on Tom Sawyer's Island past closing time by hiding in an area that is off-limits to guests. When they wanted to leave the island, they decided to swim across the river even though the younger brother did not know how to swim. The victim attempted to carry his younger brother on his back and drowned halfway across. His body was found the next morning. The younger brother was able to stay afloat by "dog paddling" until a ride operator rescued him."
Source:
http://en.wikipedia.org/wiki/Incidents_at_Disneyland_Resort#cite_note-Koenig_1994_171-29
The Wikipedia article's source is "Koenig, David (1994). Mouse Tales: A Behind-the-Ears Look at
Disneyland. Irvine, CA: Bonaventure Press. pp. 172–173." Which is a great book by the way.