I think you may have misunderstood what the agent was meaning. From what you wrote I take it to mean that 1)for whatever reason the stroller didn't get loaded on your flight to ATL, 2)Since it didn't make it on the plane for whatever reason (the baggage handlers probably forgot to look and see if there was anything to load) they loaded (checked) it on the next flight to ATL, followed by to PHI. Regardless of if it's to be picked up at the gate or at baggage claim it's still considered checked baggage. Only difference is that in your case if everything worked like it's supposed to that you would have been given the stroller at the gate in ATL.
Agent didn't mean they intended for it to be checked all the way through, just that they checked it all the way through once they realized the mistake in MCO.