Daylily rust is Puccinia hemerocallidis. It is a fungus in the family Pucciniaceae which has close to 5,000 different rust species in it. If you compare that to daylilies, Puccinia would be equivalent to Hemerocallis (genus) and Pucciniaceae to Hemerocallidaceae (family).
The grower perhaps does not know what daylily rust looks like. I would be more concerned that his comment means there is unrecorded rust in Italy but given that your pictures don't look at all like daylily rust I'm inclined to guess that he hasn't seen it. Some people call any plant problem with a rusty colour "rust" when it isn't actually caused by a rust fungus.
Plant diseases are often specific to certain plants. There are some that affect many different plants. Most of the leaf diseases that affect daylilies are not those that affect many other plants. Can you post pictures of the other plant problems?
