Thank you for your post.
Unfortunately, I don't have an immediate answer. There is obviously something that the updater sees on those two machines that is stopping from installing.
For now, download the installer to one of those machines. Quit all open applications and try to install locally. Do you still get the same problem? If so, run msconfig and stop all non-Microsoft services and try again. Do you notice anything on these machines that do not exist on the other machines, even if it doesn't make sense?
As soon as I get more information from our testers, I will let you know.
Two computers in question were not open with passwords that had administrator privileges.
Apparently, that lack of permission triggered the error message.
Curiously, dragging the installer onto the local machine's hard drive and running it triggered a request for password with administrator privileges instead of the uninformative error message I reported in the first post.
Other oddities: Some of the updated computers required a restart and others didn't. There isn't any obvious reason why some updates required a restart and others did not.