Feeding Pond Snails To Dwarf Puffer Fish. Is This Safe?

I very much doubt that any disease could be brought in by snails unless they came from something like a goldfish pond, but even then I don't know of anything. You could always keep them in a bucket of conditioned water for a few days.

There might be snails that are intermediate hosts to fish parasites, but they would have to come from waters that had fish in them.

To me, there are many "fears" that are put about that have little or no basis in reality, often based on incomplete or misunderstood knowledge. I consider that setting up and maintaining your tank properly and not introducing diseased fish constitute 99% of the battle to avoid problems.

Your liver fluke cycle is more or less correct, but it's usually just cow/sheep to snail, then to cow/sheep again etc. The usual snail host in Britain is actually more of a marsh snail than a true aquatic and is generally found in small water bodies that dry up regularly. Farmers today give their stock antihelminthics to combat this. Unfortunately these also tend to kill any insects that subsequently develop in the animal's dung, hence removing a very valuable food source for many birds and bats.

Bilharzia is a related fluke that affects humans in Africa, maybe also elsewhere in the tropics?