The style you're talking about was in use for thousands of years, and would burn almost any flammable liquid, or any flammable substance that becomes liquid at temperature (rendered/ cooking fats, for example). In the time and place that you're associating with it, they probably burned mostly olive oil. The open design is not as dangerous as it would seem, as such oils won't burn without (or beyond) a wick, but they're probably not recommended for those who might turn it over looking for a switch...

The "Aladdin" company in question was the same company that used to make vacuum bottles for kid's lunchboxes. They've been through a lot of changes, and not long ago they were bought out by a group of Aladdin lamp collectors, who have improved the quality and added quite a bit to the selection.

http://www.aladdinlamps.com/lamps/