Interesting. I'm going to play devil's advocate. Are you sure the customer replied "yes" to these? Could someone else have done it? Maybe someone (like a family member or friend) had their phone and replied "yes". Maybe they didn't fully understand the text and replied yes in error.
Does replying "yes" mean that the customer has truly authorized the transaction or they can't later dispute the transaction? I don't think there's anything in Reg E that says "if you get a confirmation by text, the consumer can't later dispute the transaction." I think the text verification is awesome, but it doesn't take the consumers rights away from them.
With that said, if the customer won't cooperate in your investigation, that makes it hard (I feel for you), but I don't think you can say these were authorized for sure. Honestly, I would call the costumer (leave them a voice message) saying "we need more info from you and if we can't get it, we're going to deny your claim." Technically, you may not be able to do that under Reg E, but I would hope this would "scare" them into action.