engineer says rotate a drawing 3"?

We started out doing a topo of an area about 5 acres or so at a power plant. As part of that, we were asked to "verify the coordinate" of a 1200' tall, 60+' diameter smokestack. It (and another one beside it, out of 4 total stacks) was captured in scan data. So, we gave the client coordinates of both stacks, derived from scan points at the base of each stack (over 10,000 points on each).

All the while, there was a lot of back-and-forth about what coordinate system to use. Apparently the plant was built in the 60's and used a "sort-of" NAD27 SPC system (their description). Also, there was a rotated system that put everything we were doing in the S and W quadrant. But, the scope gave us coords for two mons to use (NAD27 SPC). I figured out that those coordinates were raised to surface. So, we did that.

Meanwhile, the topo was extended to a laydown area with an access road. Still, under 2000' in extents.

Then they asked for a coordinate system defined by the center of the two stacks (174 feet apart), such that one stack had an assumed coordinate of 6000/4000, and the other one was due south.

We did that, but the rotation was 6' different then what they had previously. I tried to explain that we are indirectly shooting the center of the stacks, which aren't perfectly round. The previous surveys had just shot 3 points around each stack to get the center (at what elevation, from how far away?). And, remember, they are 174' apart and 62' in diameter. I believe our scan data derived centers were more accurate than whatever they did with trig.

Next, they had us survey a line of column bolts. We did this very carefully, and shot two bolts on each of 8 columns. We treated it as a deformation survey, and did everything to an accuracy better than 3 mm (0.01 feet). The onsite surveyor did it as well, but said he "guessed" at some of the offsets over to the bolts, whereas we shot each one directly.

I was in Mexico, and had to best fit a line through these bolts. I was doing it in CAD remotely on my desktop over a slow connection, so I didn't realize there were 16 bolts and not 8. I best fit a line through, and the furthest off was 0.012 feet, rms of 0.009 feet. Pretty good fit. So now they want the stack line to have this azimuth, and that would be the new coordinate system. Rotation was 20°00'24".

When I got back, I realized each column had 2 bolts, so there were 16 instead of 8. Using all 16, almost the same result, this time 20°00'21", a difference of 3". So, I used this "better" value and supplied everything to the client.

But, they said they wanted the drawing rotated 3" back to make it 20°00"24", otherwise the end cleint would freak out about hearing two different values for the rotation. I tried to explain it makes no difference in a topo (ground shots, contours, inverts, etc, nothing very accurate ), but they insisted I do the 3" rotation.

All of this to punch a large hole in the side of a stack and install a metal duct.