Can't download Mavericks installer on recent Mac. "OS Mavericks cannot be installed on this computer", which is running 9.1.

You can't. As long as a version of Mavericks is either running or exists elsewhere on any connected drives, you cannot re-dosnload.

On newer Macs reinstalling is accomplished via Internet Recovery.

Judging by the build number, it appears you have a special build of Mavericks installed and the App Store version (13B42) won't work with your computer.

Kappy - if I try to download Mavericks I get the message below, so apparently I can down load it again?

I also have a copy of the installer in my Applications folder, although it is in a folder.

Is the App Store version of Mavericks too old (jan 16) for my rMBP?

Yes. If you ever need to reinstall, use Recovery.

Yes, I see the build number. That is different from the current build, so he cannot download the current build as it in't compatible. It would work if the current build was later than his/hers.

I note that the current build is later than his/her build. In theory it should be installable.