Bad analogy. It doesnt work because it's simplistic.
Here's a Better one:
Cop sees man X. man X sees cop and runs. Cop, seeing suspicious act, tells the person to halt. Man X continues to run.
Now the cop has probable cause to pursue man x for questioning.
What was it? "Man x sees cop and runs".
That doesn't mean Man x did anything wrong, maybe X had a phobia, couldnt help it, a psyche problem, who knows, but that is what probable cause is, a reasonable suspicion upon which to act. Reasonable is the operative word on which the entire effort is just.
Does that mean that the law, who has this power, cannot abuse it? Sure, but evidence of that must be presented.
In your example, there is no probable cause, and even the correct answer, no matter what it is, is irrelevant to the matter at hand because your example is not on point.
But, in my example, there is probable cause and multiple attempts to resist a legitimate search is, indeed, obstruction, but notably in a case where there is overwhelming and continued resistance, even after it is made clear why, you continue, then, yes, indeed, whether there is a underlying crime or not, you are obstructing justice, even if you believe you did a crime, were so motivated, and discovered later that you didn't actually commit a crime. You obstructed with a guilty mindset.
Now, I"m not a lawyer. I could be wrong, So, anyone who really knows the law on this, please chime in.