OK, String height is a small factor, what's a bigger factor is the distance of the nut and saddle from the centre of the 12th fret.
First, what is the instruments, Nominal scale length?
ACTUAL scale length is the nominal scale length + compensation. This can be broken down further to be the distance from inside the nut to the centre of the 12th fret x 2 + compensation.
The centre of the 12th fret should in theory be exactly in the middle of the string length, however this theoretical scale length is dependant on theoretically perfect strings. Since strings aren't "perfect", compensation at the saddle is introduced to correct the tuning (intonation) of the instrument.
OK, if an instrument is built to theory, then the intonation (tuning) will go sharp. To correct this the saddle is placed further away from the centre of the 12th than theory dictates. If the saddle is placed TOO far away, then the intonation goes flat.
That's the simple answer.
Now this "simple" position is complicated because the placement of the nut is a factor just as the placement of the saddle is a factor.
So, move the saddle away from the 12th fret, you flatten the intonation, move the saddle towards the 12th fret, you sharpen the intonation.
At the nut, move the nut away from the 12th fret, you sharpen the intonation, move the nut towards the 12th fret, you flatten the intonation.
So, what's the nominal scale length of the instrument? Measure both ways from the centre of the 12th fret. Are the contact points where they are supposed to be? Are they closer, are they further away?
Anthony