I am not sure you will find anything really useful in the standard to convince your customer.
First I would try to clarify very fundamental thing:
Basic dimension 1.340 should not be measured at all. It is on the print (together with basic .090) to define where, relative to datum reference frame C|A|D(S), the positional tolerance zones for both holes are perfectly located. This perfect location relative to DRF, as defined by basic dimensions, is called true position of holes. So actually the measurements should show how far from the TP the actual axes of the holes are, and should not report the value of perfect 1.340 which itself has no tolerance.
Now coming back to 1.3455 measurement (assuming you have to live with this result without an option of modifying inspection report)....
According to the print the maximum distance between holes axes can be 1.350. So seemingly 1.3455 is within that. But that's true only if both axes are perfectly perpendicular to C and are exactly located at .090 from A. However if the actual distance from A is different (but within positional tolerance zone) the maximum actual distance between axes in orthogonal direction has to be smaller to stay within positional tolerance zone. So 1.3455 may in fact be outside the spec. That being said, in order to be certain whether the holes meet positional requirement it is required to know the actual deviation in horizontal direction (distance from A). Without it, your customer may be right, though relying on incorrect / incomplete data.