Generally speaking, I don't think you are wrong, although the use of the word "consent" is potentially confusing. There are multiple lawful bases with which you can use PII. "Consent" is one of the. Others include "contractual", "legal obligation", "vital interest", "public task", "legitimate interest". For the case of a private entity scraping a website, it is unlikely that these other bases would apply, but it's not impossible. It would be interesting, for instance, if some kind of police work might be classified under "vital interest". But generally, you will need consent because none of the other bases will apply.