As if they would give permission to do that.
Interestingly, some property management companies actually do, just not in this country. I read a story several years ago about one of the "Spiderman's" climbs - in Taiwan, I believe - and he was actually paid by the builder to climb the building to generate buzz and publicity. But, our tort system is such here, that no one dares give him permission - or so went the general theory of the story.