Thanks, fair point Jack1968! 

I left the note open with the intention to survey, but haven't gotten around to that yet. 

Based on the imagery available to me, there's only a fence on one side (e.g. the other side is open). That and the fact that the path is included in BGT (in contrast to the rest of the terrain) suggests it's public (municipal) grounds/property.

Besides that, on the community forum it's usually argued that "private" only applies if there's actually a "verboden toegang" or similar sign, which I haven't discovered on the imagery. 

So pending survey, I think the barrier actually suffices (for routing purposes). 🙂