So in other words, you had the square set up so it was being
used as a depth gage so to speak? When you retracted it
from the slot it read 3/8"?

Sounds to me like your blade is wider from one end to the
next. If this is the case then it's not right. A quick
trip back to Woodcraft to check it against another square or
in this case using a caliper is in order.

On the other hand, you've got a pretty rare tool there.
I've never heard of a Starrett that was out of the box out
of whack. Kinda like a stamp or money that comes from the
mint with an imperfection.

Oh by the way, the blade on these squares should be dead
nuts 3/4" wide. Your miter slots are seldom dead nuts 3/4"
wide and usually you'd be able to set the blade into the
slot anywhere up and down the length without it becoming
stuck. I doubt it's the saw table.

UA100