More than we think.
I have eaten lunch w/Amish: iceberg lettuce in July, canned sauces, such as tomato, commercial lunch meat. I have also watched them in the grocery store: flour, sugar, canned vegetables, juices and out of season produce. Not all of them farm. Some have businesses.
My husband is a medical massage therapist. He has Amish clients. A lot of depression, which can manifest somatically and, of course, a lot of congenital conditions, such as cerebral palsy. They do use the medical system. Some have pacemakers, for example. One local pediatrician used to go out to a farm and give mass vaccinations such as MMR. Entire extended families would bring their kids. Back in the late 60s we had a local epidemic of measles and people remember. This doc and another one set up a clinic that caters to Amish. One even added a birthing area just for them. There is also a midwife who works almost exclusively w/Amish, utilizing an ultrasound. She will call the EMTs and get the mother to a hospital quickly if anything untoward happens.
Point being, that the Amish are no longer as isolated as people think.
I should add that there was a severe outbreak of salmonella last summer in our Amish community. They had made homemade ice cream for a large gathering with raw eggs. There were a couple of really severe cases and many were hospitalized. A friend took van-load into the ER.
The study was about Amish rural farm children having very low rates of allergies.