The answer to this question would be: false, the organism must be not obligate anaerobes.
An obligate anaerobe organism can be exposed to oxygen as the oxygen is toxic to them. Oxygen can damage the cell by making superoxide or hydrogen peroxide. But in an aerobic organism, there is a few enzyme like catalase that protects the cells.
Obligate anaerobes don't have that kind of enzyme, that is why it can stand in the area with oxygen.
