Thank you PVGoran -- the read-only boxes have always only been "checked and grayed", and after unchecking, hitting "apply" (and choosing the recursive "subdirectory" option), and doing it for the entire Freelancer directory, I am still getting the Error Copy E6 (for both single and multi-player updates). Disappointing, I know (and the grayed checkbox is back anyways).
I get different behavior if I use the "troubleshoot compatibility" option from the icon's right-click menu. Its "recommended options" are XP service pack 2, and doing so the update proceeds for more files before hitting the bad-sounding error "Missing Freelancer E00000166, which is confusing because Freelancer is right there. To clarify: without compatibility mode Single-Player downloads 2/2 files and then hits the Copy Error, while with XP service pack 2 on it downloads 3/3 files and then hits the other error.
So a question is, what is the right compatibility mode for this? I am running Windows 7 64-bit with all the updates.