(Sorry for the slow response)
When the Triggered Acquisition checkbox is checked, background subtraction does not happen for either area or height.
Are you seeing any cases where Triggered Acquisition is turned on and it looks like background is being subtracted from the Max Height value?
Note that the peak Height and Max Height values are always going to be a little bit smaller than the actual maximum intensity point along the chromatogram. This is because all of the area and height calculations that Skyline does are done on "interpolated" chromatograms, and not original chromatogram.
That is, when Skyline is doing peak finding, the first thing that Skyline does is resample the points along the chromatogram so that the times of all of the points along the chromatogram are evenly spaced. This has a small effect on the areas and heights that Skyline reports. You can see the difference between the raw and interpolated chromatograms by right-clicking on a chromatogram and choosing "Transform > None" or "Transform > Interpolated".
Let me know if it looks like Skyline is getting the wrong numbers anywhere.