Anything that you can feel as fat on a mat would be an egriousiously fat shot on the course - one of those that goes only 20 yards total, vs. of one of those that goes 145 instead of 155.
The danger zone is shots that don't feel fat on a mat, but would be such on the course. Mats can be very misleading because even the 20-yarder will go 130 off of the mat.
Bear in mind that on grass, the ball tends to be much more sunken into the grass/ground vs. on a mat, where it sits nicely on top. Thus on grass the margin of error between thin and fat is meaningfully smaller.