I'm confused with how a dead man's switch would be useful in this scenario. If the company is persuaded to keep the transaction logs linking sim cards/phones and credit card numbers/addresses then how would we know? I don't see that as being fixed by having a dead man's switch.
At that level of 'paranoia' / privacy concern you might as assume this is an elaborate honey-pot. An unlikely scenario but certainly the safest assumption from a privacy perspective.
Churchill: "Madam, would you sleep with me for five million pounds?" Socialite: "My goodness, Mr. Churchill... Well, I suppose... we would have to discuss terms, of course... "
Churchill: "Would you sleep with me for five pounds?"
Socialite: "Mr. Churchill, what kind of woman do you think I am?!" Churchill: "Madam, we've already established that. Now we are haggling about the price”