I think that you guys are misunderstanding and mixing two different requirements regarding the MAS and the iTunes Store.
Regarding the iTunes Store, you can authorize a total of five Macs or PCs at the same time to use your purchased iTunes media; music, videos and audiobooks.
The software from the MAS can be installed on every Mac that you own or have in your control, which may include Macs issued to you and immediate family members by their place of employment or an educational institution. You do not need an account on every one of the Macs to install the software that you purchase. You only need to sign into your MAS account at the moment of installation of the software on that Mac. You will also need to sign into your account to execute a software update for the software that you installed on that Mac.