Here's what's probably happening, from what I can see.
LEDs are far more efficient than regular light bulbs in producing light, which is why they draw so little current to produce the same amount of light. The interior light circuit is controlled by solid-state devices called high-side FETs, which are basically transistors. Ford "dims" the interior lights by pulsing the circuit, not by decreasing voltage. It seems that even with the lights in the "off" position, the circuit still produces small pulses (probably because HSFETs can sense low current), and those pulses are enough to light the LEDs. The circuit was designed for light bulbs and their higher current draw.
But when you put enough lamps in parallel by turning more of them on, the pulsing disappears because the current draw increases.
Just my .02.