Joachim Schranzhofer, the head of communications at German defense company Hensoldt informed the local media outlet Bild

Here's the source that previous poster failed to include for this part: https://militarywatchmagazine.com/article/german-policymakers-concerned-american-kill-switch-disable-f35

That article is largely a pile of meaningless sensationalism with very little in the way of meaningful claims. All of it more or less boils down to this;

with analysts specifically observing that the Autonomic Logistics Information System (ALIS) system which is heavily centralised in the United States could easily be used to disable the fighters.

This is a claim that's been repeated a bunch in the armchair general circuit, but without any of the actual context, and mangled beyond recognition from what the original sources say. ALIS cannot "ground" a plane in the sense of "Prevent it from taking off at the press of a button." It's a logistics management system. All it does is track parts orders. The US could shut people out of it, which would be a massive pain in the ass, but it wouldn't actually prevent planes from flying.

Here's a source that actually digs into a little better: https://www.defensenews.com/air/2016/04/27/could-connectivity-failure-ground-f-35-it-s-complicated/

First, some context (from the article) on what ALIS actually is:

ALIS, often called the backbone of the F-35 fleet, is an information technology hub that is used to plan missions, track aircraft status, order spare parts, and manage sustainment of the plane. By contrast, legacy aircraft use several standalone systems to perform these daily functions. ALIS is the first system of its kind to manage daily squadron operations, track sustainment trends and protect sovereign information — all in one hub, according to Dave Scott, vice president of training and logistics solution business development for Lockheed Martin Mission Systems and Training.

When the previous poster's quote source talks about the mission planning system, this is what they're referring to (I'm going to skip right past their assertion that the kill switch "is more than just a rumour" because the article presents this claim with absolutely zero evidence, context, or expansion; it's just thrown out there and treated as gospel truth. Extraordinary claims need extraordinary evidence).

Anyway, from the article I cited;

Losing connectivity to ALIS would be a pain, but hardly fatal, the JPO contends. If jets are unable to use ALIS — a ground-based system that provides sustainment and support, but not combat capabilities for the jet — the F-35 is still a usable plane. In fact, the worst case scenario would be that operators would have to track maintenance and manage daily squadron operations manually, just as older jets do.

Emphasis mine. ALIS cannot "ground" planes, it can only make it harder to maintain them. And only to the extent that it's already hard to maintain existing planes like our CF-18s. This is a solved problem. We know how to do this. It's not a magic kill switch, it can't shut anything off. It's just an inventory management system.