How anyone could state this with any particular confidence is beyond me. The truth is, when someone votes by mail, you have no idea who filled in the ballot. How could anyone possibly collect metrics? No one can possibly say what's going on, unless you trust the populace at large, which not everyone does. Many countries have systems for dealing with this. In many countries, they ink your finger to indicate you voted. Why not just do that at physical polling stations.
Honestly, mail-in ballots are very difficult for me. They get mailed to you, and by the time I finally have a chance to sit down, I often have to go searching for where it went / whether my toddler put it somewhere. On the other hand, when I voted in person, I would just go to the polling booth in the morning and be done. Super easy. I don't understand the desire for pure vote by mail.
One year, I didn't even receive my ballot, and it was difficult to get a replacement. Whereas, when I lived in CA, it didn't matter. You show up to the polling station (which is conspicuously noted), and just vote.