I copied the files, wanted to update - blank page and only "access denied" alert.
WTF?

OK I got it. There was a problem when copying zp-core/setup/index.php file... I had to delete it on the server and transfer it again.
EDIT: And some other files in the zp-core/setup folder...

That sometimes happens via FTP for whatever reasons when uploading a lot of files at once. Or it was just wrong permissions.