Open string harmonics can -ONLY- be used if the guitar is set up properly and correctly intonated. I've encountered many guitarists that aren't even -aware- of the fact that if you change the tuning or the gauge of strings, the harmonics need to be 're-tuned' by adjusting the saddles in the bridge. Proper intonation adjustments are paramount for proper sound all the way up the fret board as well as being able to use harmonics to tune the guitar to itself.
A second, less severe, issue is that changing tension on a string inversely affects the tension on the other strings. So, tuning a flat low E, for example, will slightly relax the other five strings and cause them all to go just slightly flat. If the entire guitar is flat, I like to tune the low E a little sharp, adjust the rest of the strings, and come back and see how much the low E "flattened back out."
Tuning a guitar is as much an art as it is a science.