Here’s the thing: there is no reason I can think of for the State to verify signatures after the petition has been certified, by knocking people’s doors and demanding proof.
When a petition is submitted, the sponsoring organization first looks at it and makes sure all the i’s and dotted and the t’s are crossed, and then makes sure it has plenty of extra valid signatures to account for challenges by another organization, or I guess by the state. That’s why you hear about 1.5 or 2x the signatures required being submitted. They can see before submitting how many are going to be challenged because the name or address is printed illegibly, or the person does not appear on the voter rolls, or required information is missing.
An organization (or the state) can challenge particular signatories, and at that point, the sponsor has the option of proving that the person is actually a registered voter, and if necessary that the signature is close enough to the one they used to register. Or, they can just opt to let the challenge stand because they’ve got like twice as many signatures as they need anyway. If enough signatures remain after the challenge process (which has deadlines, too) to put the question on the ballot, it gets put there, end of story, right?*
Any signatures that were being challenged would already have either been removed from consideration by this point, or they already would have been investigated, found good, and counted. The question is already on the ballot.
Election police have no reason to show up at someone’s door at this point. Whether or not their signature was counted has already been decided!
Voter intimidation seems to be the most obvious reason for the election police to be knocking on doors. But another reason might be that “evidence” gathered on those people who try to cooperate might be used to invalidate their vote, particularly for mail-in ballots. Gotta match those signatures! If they really were investigating fraud, those interactions would surely be postponed until after the election for the very reason we are all outraged by this stunt. And even then, I would think there would be a very high legal bar to clear first.
*Except in Arkansas, apparently, where they can throw out petitions due to a missing photocopy that isn’t required, even though the affected signatures could have all been left off because they already had so many for the abortion question. Calvinball rules.