I recently saw a quote from an expert which said it takes three atoms to form a molecule. It seemed clear from the context that they were including (and in fact referring specifically to) molecules made up of two of the same atom. So to make one molecule of O2 you need three O atoms to participate in forming the molecular bond, you can't just put two O atoms in a box and make O2. Is this really true? If so, why?
There are different processes of molecular formation. Each of them has its own efficiency depending on the environmental conditions and the kind of molecules and reagents. A quite efficient mechanism is that of exchange reactions: a molecule $AB$ interacts with molecule $CD$ to end up with a molecule $AC$ and a molecule $BD$. In the case of diatomic molecules (like O$_2$) another efficient mechanism requires two approaching atoms and a third atom whose role is only to "extract" the excess energy with respect to the bound molecule.
Finally, there is a third mechanism, usually less efficient, but sometimes the only available, which is the radiative association, i.e. the case of two approaching atoms and the release of the excess energy through photon emission. A situation where such a mechanism dominates (du to the low density) is the molecular formation in interstellar clouds. In usual lab conditions triple collisions are more efficient and this is the probable reason for the statement you have read.
Two oxygen atoms would just scatter off each other. Yes, there are potential surfaces with a minimum where a normal O$_2$ molecule sits in a bound state.
But two oxygen atoms have no way to get rid of their energy. If they are on an attracting potential, they will accelerate toward each other, move through the minimum, and bounce back. An elastic collision.
It needs a third to absorb energy.