I think iD is wrong to assume that - though it may be appropriate in most cases. Here's a discussion on the subject - https://community.openstreetmap.org/t/tagging-a-way-that-has-a-road-marking-for-pedestrian-priority-cycle-slowly/7767 .

So I suppose, whoever is there next can check the signage (painted on on tarmac in big white circles at all the entrances to the park (last I looked)) and flip ti back to highway=footway if needs be.