In the example case, the earth's rotation is producing the apparent observation: it's the cause, not a separate phenomenon that happens to coincide, or that might be indicative of a deeper relationship. For something to be a coincidence, it must be otherwise unconnected causally, which is not the case if the reason you found a ~24 hour period is that you forgot to account for the earth's rotation.
I respectfully disagree (without attempting to say you're wrong!) about the definition of coincidence and the requirement of being non causally related. If I'm riding on a bus and the light poles going past line up with my music, that's a coincidence even though they are cause soley by the bus motion BPM matching an essentially random choice of song BPM.
What I'm describing is an artifact in your data that is caused by the motion of the earth.
To give a more concrete example, suppose you measuring the brightness of a trans-neptunian object, and observe that the brightness changes slightly with a period of about 1 year. You might think it has a non-uniform albedo, and a rotational period of one year, when in reality, it is just brighter when the earth is closer to it.
