Put a high quality straightedge against the fence and look for gaps. That should end any debate about the fence being the culprit. Hardwood is not the best choice for jigs and fences. I prefer finish grade plywood with 9 or more layers for the best chance of keeping things straight and square. Wiping a shellac finish on both sides helps to keep jigs flat as well.
Put one leg of your square against a STRAIGHT fence and draw a line against the edge that goes out at the 90. Now flip the square over and look to see if that leg aligns with the mark you just made. If it does your square is fine. We can't all afford expensive machinist's equipment.
You can adjust that type of square if it isn't actually square. Use a punch and a hammer on the face of the tool in the corner where the 2 legs meet. Punch the inside of the corner to make the legs separate, and punch the outside of the corner to close them.
Buying a nice square doesn't have to be expensive and it doesn't have to be a starrett.
US made, factory blemish squares. Only cosmetic issues, and they are 100% square. Shipping is typically pricey from them, but if you order a few things at once it's not bad. I've got 2 squares from them.
Just a heads up - I hate to poop on the party, but I got a small square from Harry J Epstein and it wasn't square it was out by probably .003 or .004 over 4". Either that or my starrett is out, and I'm guessing it isn't the starrett. Just know there is a risk when buying. Some are probably good, other probably aren't.
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