Thinking about it, Truth doesn't preclude further research into combining AV with divine power as has been suggested.
Truth research requires the combination of four things. Mathilde's astonishingly keen Windsight, AV, Aethyricly sensitive recording crystals, and a divine relic. Without all of those things, it's not possible.
That means that, even if we take the Truth path, we should still be able to do things like give a spellcasting priest a jug of AV, ask them to channel their god's power into it, and see if their god can produce a larger than normal miracle thanks to not having to push power through the bottleneck of the priest's soul. That in no way reveals that Mathilde can fingerprint the gods, or even hints at it.
As a result, there isn't one of the opportunity costs that's being suggested by some people.
This kind of side research might also mean that the gods have more reason to forgive Mathilde if she is caught fingerprinting them, as she's also the source of something that can significantly empower their mortal agents.