So either the swap happened on the residential and, having then worn the shoes at a later date, no one noticed that a) their child's shoes were suddenly too big and now had insoles when they previously didn't or b) their child's shoes are smaller and no longer need the insoles and extra socks.
Or both girls had their own boots until the later walk at which point something happened. A child couldn't go home with only one shoe so I'm assuming they changed shoes for this walk. That leaves it open to either a) your daughter taking the wrong boots home and the other child not taking any home or b) the other girl not taking any shoes home, with your daughter still taking the wrong ones.
Either way neither girl, or parent, covers themselves in glory and you have no idea whether the other child actually lost the boots or whether your daughter took the other boots first and the other girl left your daughter's at school. However you seem to want to place all the blame at the door of this other child when, really, both children are responsible for the lost boot because neither of them could keep track of their own belongings. Your child is as much at fault at the other and could possibly be more so, but I doubt the whole story will come out.
You knowingly have someone else's boots. Give them back. You should then speak to your DD about keeping track of her belongings and you should be a responsible adult and label her clothes.
I do suspect that you won't return the boots and will forever provide updates that make the other family seem like CF, as you have done multiple times already.
I hope the other child has no skin conditions that could be passed to your daughter through the knowingly wearing of her boots.