As for actuaries, in the US, the GINA law prevents health insurance companies from using this data. I think legal protection is much more important than attempting to hide my DNA.
I agree, if you can't justify trust with reason then it's hard to trust your argument that relies on trust. Trust can be broken, and your stance doesn't address that concern.
With your own "trust can be broken", you could conclude that you should distrust "with reason" (hey, it was broken) — basically, flipping it is an equally sound stance.
As a rule, I trust people, keep private stuff not easily aggregated (eg. I might talk some stuff over lunch, but will not email it to the person so they have it on record), and I am quick to distrust people once they fail me. Legal protections do matter, because they discourage misuse of unintended data sharing.