just some back of the envelop calculations. Since angle of view is a trig function and not a linear one, we should expect some variation of the rule with different focal lengths. From about 22mm focal length on a 35mm camera, you will need to add a correction factor to the denominator greater than 1. I assume that the original rule was for a 46.8 degree angle of view.

Taking these corrections into account, a more precise rule of thumb should be about 1/250 for a 200mm lens and 1/20 for a 25mm lens. Given that most cameras back then, and many now, don't have 1/200 as a shutter option, nor a 1/20, Using the standard rule of thumb for focal lengths greater than 22mm on a 35mm camera should be fine. Smaller than 22mm, you would have to get near fisheye territory to need adjustments.

If you find the rule works for you, no need to tweak it for different focal lengths.