Hi Handcrafted,
I think there is a little bit of confusion as to what is classified as the "main computer". You are totally correct that you should only install Method on the computers that actually physically opens QuickBooks. Therefore, if the QuickBooks server is only housing the database, you should NOT install the Method Engine on the server. You'll want to install the Method Engine on all other computers that actually open QuickBooks, that way you have real-time sync capabilities throughout the day.
The main computer (or better known as the computer that is left on the most) is the computer that has QuickBooks installed and is the computer where the initial sync was made. This computer is the one to be most concerned about since if this computer is off, the rest of the computers won't be able to sync changes to QuickBooks until this computer is turned on again.
I hope that helps and Merry Christmas!
Danny