I'd guess the inaccuracy lies with the calibration of the Haimer. I guess the first question that seems pertinent is: did you calibrate your Haimer? If you didn't calibrate it: it's not likely to be accurate.
A test you can perform with the Haimer is to find the same surface with it rotated at different angles. For example, use the Haimer to find the left side of your fixed vise jaw and zero the DRO, then rotate the Haimer 90° and find the exact same surface. The DRO should read close to "0". Do the test again at 180° and 270°.
Take a close look at the stylus. Is there anything wrong with it? Push on it to see if it bends/flexes more than it should.
Not too long ago the ruby ball of my touch probe had cracked in half, but the split line was real close to being in line with the X axis, so it looked OK if you only glanced at it quickly. Maybe the ceramic shaft of the OP's stylus got cracked somehow.
I got coolant in my Haimer and it stopped working correctly, the mechanism got gummed up. Is the Haimer "spongy" in any way?
I'm going to guess your calipers aren't the problem, but an easy way to eliminate that potential problem is to simply use a block of a known size. Like that 1-2-3 block.
That's a good call! Perhaps Gerry Kmack ended up with the wrong model of tip attached.
But is that something that will be in the tool table? Because of the way Haimers work, I can't think of a reason for the ball diameter to be entered into the software.