The "sunny f-16 rule" doesn't just apply to sunny situations, and it isn't a rule either. It's basically remembering the simple guide included in a box of film. It's only f16 when it's sunny with distinct shadows and you're not on the beach or in the snow, or similar situations. In that case, you increase the shutter speed one step.
If it's hazy sunlight -- thin clouds or haze -- but there are still some shadow, then you open up to f11.
If it's bright but there are no distinct shadows, open up another stop.
It's goes on as the light gets dimmer, and it's pretty accurate -- and easy to remember.
And if your memory isn't what it used to be, just keep the sheet in your pocket or wallet.
And it's not against the law to bracket -- at least not yet.