It's mostly not the fee to speak, even though a mere $1 per vote could be too expensive for some petition-spamming efforts: 100k payments from the same account would trigger suspicion, and creating 100k legal payment accounts (paypal, google / apple / samsung pay, venmo, etc) just to pay $1 per vote may be onerous.

I mostly say about giving a ton of identifying info so that your vote can be reliably tracked back to you: not only email (with a one-time link to confirm the email works), but also a phone number, postal address, maybe even some government ID like SSN or driver license number. It removes any expectation of anonymity from the vote or signature, and this is by design. Fraud of the kind the article mentions would be easily detectable by a random check of 1-2% of the signatures (and more is suspicious patterns are noticed). As a side effect, it would make a vote or a signature a much more conscious, committed decision.