How to explain these two discrepancies between BLS OES wage data and salaries of pro athletes?
This may not be the complete answer but I believe this is a major issue:

It is extremely difficult to get famous and rich people to participate in surveys. They have handlers that prevent surveyor access. They have multiple phones numbers and homes that makes it difficult to find them. They also have complex affairs that may make it difficult for them to easily summarize. For example, having a complete picture of sponsorship income can be challenging and almost no one knows what a fair value is for their accumulated pension. 

In summary, I assume that most of professional athletes are not covered by the BLS survey. Instead, it is people of more modest income, like minor league athletes and golf pros that are actually getting picked up.