That's interesting what they said about the ionic strength. I did a bit of research, and generally, pH measurement methods such as reagents or probes are designed to provide accurate pH readings for highly buffered solutions (solutions containing a considerable concentration of a particular ion.) However, when the solution is less buffered, the accuracy of this equipment become less reliable. It can be considered that soft water (water containing fewer calcium and magnesium ions) is less buffered than what is considered hard water. Since soft water contains fewer ions, the ionic strength becomes less significant. This might be a stab in the dark, but my guess is that the water company might use a device such as a pH probe or a chemical reagent. However, since the water in your area is quite soft, there might be the possibility that their devices are rendered less accurate in comparison to your indicator strips.
It would be interesting to see what kind of reading you get if you were to use a pH probe instead.
EDIT: The one thing that I find to be very bizarre, however, it how your reading and their reading are 2 - 2.5 pH units apart. Generally, the maximum error of a pH probe or a reagent under such conditions (low ionic strength) is 1 pH unit I thought...