I thank you all for such a lively thread. At times like this, I wish we all around a campfire or 1080 and discussing it. I am with many of you when you say that +/- 0 is square. In my early days, I wondered how the 4th corner wouldn't fit together, the other three worked fine. I think we have all been there. In the more recent years I have come to realize that 1/16th off is way off. I use playing cards for a lot of the router table tasks. If I had to pick a deviation that us allowable, it would be the thickness of the playing card (particularly the heart face cards.)
Ed Bennett gave me my first engineers square and with it his encouragement to align things so that the end product was "dead on." I think of my tools as part of a system. Every tool is aligned so that every component is "right on."
When Elena and I were practising with the then new to the shop Domino Joiner, she was surprised and delighted that the side with 11 mortises came down and fit over the 11 tenons so snugly. We were trying to prove to ourselves that we could use the tight mortises all the way down the line and have the pieces slide together. It did and it was a nice feeling.
So square is light pregnancy, I guess. You can't be a little bit pregnant.
Again, thank each and every one of you for your thoughts.