Hmm, go back and re-read the O.P. post. It no where says "private" versus "public".
Yet anyhow, I agree that there is a difference between the two, in actual practice.
But question for you: How about "private" property, when it's nameless faceless coorpration land ? For example, where they're tearing out some old structures to make-way for the next K-mart being built in your city ? Or row-crop ag-land owned by some mega-company 2000 miles away? Those examples versus someone's personal yard. Each, yes, is "private property", yet with a distinct different flavor. Eh ?
Owned by a faceless corporation or an individual, doesn't matter, I still get permission for all privately owned property.
For example: There is a large office building that dates back to the early 1910s in town. At one time it was a public school and later converted to an office building. It is abandoned looking, fenced in, and owned by a large 'faceless' commercial real estate/leasing company. I could have easily been like the other goons and climbed the fence to hunt it when no one was around. Could I have gotten away with it? Probably. But I am a better person than that, I respect property owned by others.
I found the local office for this company, which was close to work, and located the agent in charge of that property to ask him permission in person. He was hesitant at first but I offered to pick up the garbage in the grass around the building, to which he gladly gave me permission to hunt it at that point, and even his business card in case anyone questioned why I was there. It only took me 10 minutes to fill two large garbage bags and I got a good month worth of hunting and a found some really good stuff there. After hunting the property I sent him a quick email showing the cleaned up grass and thanking him.
He could have just declined my request to detect this property.
How would that have been any different than a home owner saying no to my request to hunt his property? If a property owner says no, you take note and move on to the next place to ask permission. Maybe ask again later on if the circumstances or owner changes.
I find it easier to get permission to hunt a property when you throw some incentive in there. If the place is overgrown, offer to knock the weeds down with a weedwacker. Not only will you do the owner a favor but you make swinging your coil much easier. Offer to pick up garbage, it doesn't take very long and nobody seems to object when I mention that. Even those 'faceless" owners will consider a deal like that.
Personally, I would never hunt with someone who trespasses. Eventually they will get busted or have a run in with the wrong pissed off land owner.