Truce offers of any kind

You are either not reading or just want to stir the brown stuff

The text is entirely correct -

Lend a hand
Use truce offers of any kind on your friend’s islands.

So the win condition for that specific quest is you need to use 4 truce offers on your friends island, whichever truce offer u use will complete teh quest

The quest does exactly that

You are trying to connect that quest to the other quest which is partycrashers with suboption talk it out

Peacefully resolve the issue of the party crashers using appropriate buff.

No other quest line in game works like that and it is far from logical what u state

You can be on any version of the camps, if you go and drop 4 truce offers on someone with a lower camp up, the lend a hand will register complete with the lower buffs - So the fact that the camps you are swapping doesnt accept the modest truce offer doesnt mean that lend a hand os broken or is misleading

Lend a hand doesnt care which truce offers you use, it is up to you to find the ones that can be dropped on the camp or find a camp that you can drop the ones u want to drop on it