I agree with you about them being safe due to the security zone set around them. It's supposed to be 3 miles ahead, and 1 mile abeam and astern. In my port, the zone around the tanker while offloading is 400 yards, which extends accross the river onto land, but boats are still allowed to transit through.
The study that details all the danger involved was formulated around a lot, repeat a lot, of assumptions. To get the ideal circumstances for an explosion are very nearly impossible outside of a laboratory. Oil tankers and tankers carrying gasoline present a much bigger threat, both damage wise and environmentally.
By the way, if you spray water on LNG, the water explodes into flying icicles. Pretty cool actually.