Your title describes the situation well; your finger made a closed, not short, circuit thus pulling the pin high. If you had the pull-down resistor connected then I doubt it would have worked.
PS- don’t connect LEDs w/o resistors to the output pins. That’s a good way to damage the pin.
Your body will pick up electrical signals from overhead lights and nearby wiring, and will inject these into circuitry.There does not have to be an obvious physical connect to “ground” as there is a capacitive one.
You are “in the circuit” but weakly via capacitive coupling. Akin to the touchscreen of a phone. But adding a pull -down or -up resistor to the input pin should overwhelm that weak coupling. So I ask what do mean, what are you seeing when you say …
and is interfering with the button circuit when it is connected.