They have mate. The article by Miguel Delaney is pretty authoritative in that respect - they agreed a deal in principle for him 10 days ago, and our interest only started after that.
As per Delaney, Palace used us to get Arsenal to up their bid, but both they and Eze knew that Arsenal were in for him - and probably would close the deal if we showed any sign of approaching an agreement.
We did, and Arsenal moved. But the actual verbal agreement with Palace/Eze was done 10 days ago, which means negotiations would have taken place earlier this summer.
If anything, it's a lapse in our intelligence - we should have known this before going into the whole dog-and-pony show. Typically, that is the fault of the DoF, whose job is to maintain domain awareness of this sort of thing. Hence why I think Lange is cooked come window's end, and Paratici probably slides in afterward.