It's an AC circuit. The DC resistance you'll read is very low even if everything in the 6.3-Volt AC system is perfect.
I do remember one of these 455 kHz IF transformers that had the wire come loose inside on the side connected to a tube's plate circuit. The wire has insulation but not much. It would rub against the inside of the metal can and blow the 2.2k plate resistor. By the time you had turned the radio upside down to fix it, that wire would pull back away from ground just far enough to clear the short. He got tired of this and wired a 10-Watt resistor in its place. Next time that wire touched ground inside the can, the IF transformer smoked. The half-Watt resistor had been protecting the loose wires inside the IFT when it smoked. The 10-Watt resistor let the IFT's wires smoke. They protected the resistor.
Did finally clear up what was to blame for this symptom on that occasion. The IF transformer's primary winding was dead open.
73