Most natural phenomena are minimum phase.
If the strain gauge cartridge is also minimum phase (why wouldn't it be!) - then a flat F/R implies correct phase, as the relationship between amplitude and phase in a minimum phase system is symmetrical....
As long as you are not using digital linear phase or maximum phase filters, any mechanical adjustment or standard electrical filtering/EQ will be minimum phase, hence the simple old fashioned flat frequency response is a valid measure of phase correct behaviour.
It sounds too simple to be true, but in this case stick with occams razor....
The strain gauge test report does not look at phase....
But they are measuring an analogue system using analogue (which implies minimum phase) systems...