I think another clarification is needed on this. First, what is the medicine in your Medicated Feed? With a few exceptions (mostly feed meant for Broilers not chicks that will become laying flocks) the medicine here in the States is Amprolium. Amprolium is not an antibiotic, it it a thiamine inhibiter. It does not kill the the Coccidiosis bug, it inhibits its reproduction. It allows a few to reproduce but inhibits the mass reproduction that typically causes the problem. A few of those bugs in their system will allow them to develop an immunity to that specific strain of the protozoa, usually in two to three weeks. It's when the number of those bugs get out of control that coccidiosis causes problems. Those bugs thrive in wet soil or dirty water if they have manure in them. If you keep the water clean and their living area dry Coccidiosis is unlikely to develop.
The Amprolium-medicated feed by itself will not give them immunity. The protozoa has to be present before they can develop the immunity, and that immunity is only to the specific strain present. If your chicks have contact with the ground they will get that exposure. A broody hen will give them that exposure. But an all too common occurrence is that people keep their chicks in a sterile brooder where they are fed medicated feed but are never exposed to the Coccidiosis protozoa. When they leave the brooder and hit the ground they switch to a non-medicated feed just as the chicks are first being exposed to that bug. They have not developed any immunity because they have never been exposed. If conditions are wet they can easily come down with Coccidiosis.
Like Wyorp Rock, I feed my brooder-raised chicks dirt from the run where the adults are to introduce that bug, usually the second or third day they are in the brooder. Since I keep my brooder really dry and change out the water daily I feed them more dirt every three or four days so that bug is constantly present so they can develop that immunity. In addition to them developing the immunity they need before they hit the ground I figure I am giving them grit plus exposing them to any probiotics the adults may have.
The main point is that medicated feed does not give them any immunity. That bug has to be present first.