That's not true, and things that happen in the real world is different from the antenna theory. I tried creating a small loop antenna for my AM radio but even if it worked without a ferrite rod, the signal was weak. But when I used a ferrite road antenna with a ferrite rod transformer (16:1), the reception was mind blowing.
I know that to get a good SWR value below 2, the impedance should match. But there is a catch with 16:1. I won't take the impedance of the main loop for granted because that could be anything. But the transmission line will be connected to radio using either coax connectors (50 ohms) or twin lead (200 ohms). Now, incase of 50 ohms, the antenna needs to be 16 x 50 = 800 ohms (for 16:1 transformer), but what if the impedance is higher than 800 ohms. Even if it's 1600, the output will be 100 ohms. So, a higher impedance won't cause much problem for 50 ohms but less than 50 ohms will be a problem.
But for the AM, a 200 ohms connector is used because 16 x 200 = 3200 ohms or higher impedance loop antenna can be used.
But if I am not using 16:1 then I might need to use only a 200 ohms antenna and that may not be having too many windings to get good reception.
That's why a 16:1 transformer can let you connect a higher impedance antenna.