(This is on the first cup of coffee - bear with me.)

3/16 over the width of a bed (single?, queen?, king?)
isn't much - a slight error either way could be additive.
Say you have a parallelogram from the slightest non-square
cut - 1/32 of an inch, but it's consistent on every board.
That will pass the finger test on long boards as you line
them up one way ( /___/ ).
But you are really out a 16th (1/32 + 1/32). Other end of
the board is the same way. Edges and center measurements
are all identical, and so is corner to corner.
Now flip a board ( \___\ ). Measures the same way - good.
But now compared to each other, you have -
/___/ and
\___\ , where you have doubled the error - as compared
to each other.
This assumes 1/32 on same width boards - you have
different widths so the difference would likely vary.
Now if you were also a 32nd shy on one and over a 32nd
on another...

I would have to clamp the boards together to make sure
a 6' board didn't shift until I got to the other end to check.
Then I'd flip a board at a time, re-clamp and check to see
if I could spot the difference.

Or it could be the phase of the moon.
-J