That's true. However, I don't think a thorough knowledge of decompression issues is required in cases like these. Understanding that it can happen, and what some possible symptoms are is enough. First aid is usually the same. Out of the water, and on oxygen. Even if the oxygen doesn't help the particular variety, it doesn't hurt.
In water recompression can theoretically work, but is usually not recommended as it's not as easy to control. I can understand doing IWR when in remote areas where a chamber is not likely to be found nearby. Not the case in this area. In most cases it's not recommended as more harm can be done. The fact that it was attempted seems to indicate that there was, at least, knowledge of potential problems.
Each one has different rules, but often there are different categories for Freediving and Scuba. The tournament organizers do not require any classes specific to the tournament. Usually registration and a Captain's meeting would be required. Depending on the tournament, there are likely also to be limits on distance/depth, and species to prevent riskier deep dives.
The reference to the tournament win is not to imply that advanced deco theory is required, but rather to indicate that this appears to be a family that is familiar with diving and spearfishing. I have no idea how many people are in the family, or how many dive/spearfish, but it appears to be at least two. The mother is on a local Spearfishing Facebook group.