With strong illumination, lots of algae growth, a trickle filter with air pumped into it, and a good skimmer, you can achieve mild oxygen supersaturation conditions in a reef tank. This is safe and generally beneficial to your animals, but on the other hand, not at all necessary to have a successful reef (and nobody uses trickle filters anymore, anyway.) Dangerous oxygen supersaturation, which can actually hurt fish and other animals, is highly unlikely with systems and techniques typically used by hobbyists, although I believe a weir might be able to cause this if used incorrectly.
Use of ozone, by the way, does not increase your dissolved oxygen levels directly. It may help to do so indirectly, by oxidizing dissolved organic compounds which would otherwise use oxygen to decompose.