Are you saying you are cutting the mat opening exactly to the print size?
Not at all--for nominally 8x10 on an 11x14 mount, I prefer a 1/4" reveal at sides and top, and 5/16 at the bottom (for the signature). I agree that with larger reveals (1/2" or more) the precision issue is less troublesome, but I happen not to care for the look, as it seems to make the frame too small. Going up a size would fix that, at the expense of making the whole thing a bit pretentious, the way some art students put a 4x5 contact print in a 16x20 mount
The problem for the frame shop is not cutting the mat, but measuring the print to the required accuracy and then entering the dimensions with enough precision. The print is not always perfectly square (although I do the best that I can) and often ends up not measuring an exact multiple of 1/16", which seems to be the software limit for the computerized cutter. Since I register the top right-hand corner of both the mat and mount before transferring the print edge locations to the mat, the absolute dimensions don't matter, and if anything (print, mount, or mat) is slightly off square, this method compensates and the result visually acceptable. Believe me---an error of six hundredths (about 1/16") is
very noticeable!
I hope that the foregoing is understandable---it is easier to demonstrate than to explain.
I have nothing against either manual or computerized mat cutting, and use both when I can. But for my personal things, I like to be able to trim off a distracting bit along one edge of the image, and still have the mat opening exactly fit the print.
With a nod to the original post: American Frame cuts all manner of mats to order (including oval!) and offers both Crescent and Bainbridge conservation matboard. I have found them to be quite conscientious, and easy to deal with.