Wrong. Almost every home/farm has a landline. If they're running a business many time they have what they call a "black box" which is a cell phone type transceiver with a regular landline type phone attached to it. It's battery powered and I've seen them mounted in lunch boxes, briefcases, toolboxes and other non-descript type enclosures.
Some married men have cell phones, but not the smart phone, most of them are the older flip type phones. Just about every school teacher has a cell phone, which came about after the Nickel Mines shooting a few years ago. They recognize the need for the safety of the kids, since at that incident a young boy ran to a neighboring farm to use the phone. Many of the teens do have smart phone, but when they're done with rumspringa or when they get married, the smart phones are gone and they get a more "traditional" phone.
I called my friend yesterday morning about something I wanted to give him. He called me back around 8:30pm, so I guess he was busy all day. I know a family where the father, and the two oldest boys are firefighters. There was a huge fire in their area a few months ago and I texted the oldest boy and said "I know you guys are at the fire, please becareful and get home safe". He texted me back pictures of the scene.
I've joked with my wife that more amish have my cell phone number than english. There still some more traditional Amish that still have the "phone hut", which is a small shack at the end of the farm lane, normally out near the road, and there are still some that don't have phones at all, but that's getting more and more rare as they've come to realize that phones (landlines) are important.