It turned out I needed to enlist the help of hosting support to change the protection on that file. No idea how its protection got changed. But once it was reset to 0644 the 4.1.0 update completed with no problems.
I have the same problem, although I am trying to update to 4.1.0 and the filename is not called out in the error message. I checked and confirmed that class-bp-phpmailer.php’s protection is 0000, so I am guessing this is the problem file. But I can’t seem to change it back to 0644 in my file manager, it just seems to reset itself to 0000. Do you think it is possible this class file is locked by a plugin?