How do tell that I'm not using an UNO?
By the behaviour of "pin 13".
The problem you described is due to the presence of a LED directly connected (by a resistor, 330 ohms on the original Nano) to pin 13, which pulls it down. To overcome this as a pull-up you have had to use a sufficiently low resistor. It does not have to be as low as the 330 ohm because the LED already has a voltage drop which is relatively close to the half-way threshold.
The UNO design deliberately avoids the problem with pin 13 by providing a high-impedance buffer to the LED - actually an op-amp. It is in fact, such a high impedance that if your code does not define pin 13 as an output and does not attach something to it to pull it down, the LED will light or go out quite randomly. This is never noticed initially, as the board comes with the "blink" program loaded, but it "spooks" people when they run another sketch which does not use pin 13.
So the fact that you had such a problem specifically demonstrates that you are using something other than a UNO. :grinning: