Two conditions for the chain we got in the header pre-sync are:
- to have minimal chain work
- to be within 1 day worth of work from the active chain tip's work
When we start Bitcoin core node for the first time, the active chain tip is on genesis block. The chain we get in pre-sync has an extremely large amount of cumulative work. So, it will pass the first condition, but how will it pass the second condition? It will be much more than within 1 day worth of genesis block work.