I disagree with the more recent PPs and agree with earlier PPs.
Both girls could have accidentally swopped (or there could be a third child/pair!) Other child could have been the one that took OPs DDs! She sounds incredibly careless. If it all happened when away she'd have asked teacher that she only had one boot or no boots!
For whatever reason, other DC has been wearing swopped boots since then and has been careless in subsequently losing one of boots- as parents would have noticed otherwise when unpacking.
If had been genuinely lost on trip parents also would have noticed within a day or two after trip. It wasn't.
Now other dad wants to swop one boot for two a month later with a child that may not even have his DDs original pair, only because his DD has lost one she had in her possession! His DD must have worn or taken them into school and lost if one was found at school. After residential trip the belongings don't go straight into school, they go home off the coach.
YANBU to reply
"Sure, if you believe you mistakenly have my DDs boots , bring the pair into school to show me, I will check them and ours and swop if that's the case."
(If not I don't know how I can help you, as DD had a pair not one when it seems that your DD took them)
It's not your fault his DD has lost a boot and is suddenly unhappy They haven't taken any due care of the boots she had and has responsibility to do so . It's for them to replace like for like if you do end up swopping back. It's a bit meh, what can you do?
All this talk of thievery is ridiculous. No one stole anything. OP is not a CF, the other dad is and he knows it!