In game 845605, Constellation and Duguay Trouin are grapled, and both are anchored by bow (or stern, I don't remember).

Now, the melee box for Constellation does not allow for OBPs. I can only check NBP, DBP, or TBP. (The TBP options include Duguay Trouin).

I have never come across that before, hence my guess that it has something to do with the fact that we are anchored.

I cannot see anything in the ancoring rules about this. The only thing is that a ship may not engage in melees when up-anchoring.