I bumped my head against that and I figured it was time I came into the community to see if Apple experts can give some advice on what to try.
I did the following:
The AD Personal Folder is created for users, with Modify + Change permissions on all subfiles and folders.
I made sure that the file is not highlighted in the Finder and I also disabled the generation of thumbnails.
I've also disabled thumbnail registration in Photoshop thinking that the file may have been locked.
Alas, these things do not seem to change much, I checked the permission on the file and it says that my user has read / write access. (From the end Mac)
It should be noted that we use a local account to connect to Macs, but then to a server using their domain credentials. We made sure that the keychain is cleared from other usernames and passwords.
We use Mojave with Windows Server as an Active Directory host.
I've used the SysInternals "Handles" tool to see what keeps the file open. I did not nailed it, but when I open the file in Photoshop, it sometimes happens to have two open handles for the PSD file, one with seemingly no permission, and another with RD.
When this happens, I notice that there is an identifier with an RWD permission, but it does not tell me which program opened it because it is accessible via a share.