Apparently MAMP has upgraded its installation script to run Apache as the installing user instead of an arbitrary _www. A good move, too bad I was unaware of this, my apologies.
I just thought of a couple other possibilities. Do you have any kind of security running? On localhost I’d think not. Check all .htaccess files along the path and insure there is no rule that could be restricting access.
I assumed you were uploading an image while editing a post originally published August 2015. If so, creating the /2015/08 folder is normal behavior. If not, more is broken than error reporting.
I agree with your latest assumption. If all permissions are in order, the error message itself is suspect. Are you using WP in its default state — no plugins and one of the twenty* themes? If not, try that and see if it makes any difference. A long shot, but we’re entering drastic measures territory.
The next step after that is manually reinstalling WordPress. If you’re comfortable coding PHP, you could trace through the image upload process and try to locate where things go wrong. More than likely you’ll end up at mkdir() returning false, which is expected and doesn’t really help us any. But if it is something else, this would find it. It’s a very tedious, time consuming process that even an expert coder would be reluctant to undertake.
If reinstalling WP fails to help and you understandably skip the trace process, then MAMP itself is suspect. I did have trouble once with PHP in an very similar LAMP installation, so it’s not unheard of. You’re not using a beta version of MAMP are you? I don’t think there’s much we could do to debug MAMP other than reinstalling. You could try reverting to one version earlier in case there’s some newly introduced bug that only manifests itself in rare cases.
You could possibly consider one of the alternatives to MAMP if the problem persists despite all of our efforts. Depending on the root cause of this, it may or may not help.
I’m truly out of ideas now. My biggest fear is I missed something simple and had you go through all of this reinstalling for no reason. Since privileged access to people’s installations is beyond the scope of these forums, it’s easy to miss something that sitting at your computer might solve. Consider getting an expert local to you that is trustworthy to figure this out for you.