I think it comes down to the fact that the bet is correct if "worse hands call" and "better hands fold" is a bit simplified. It's the mistakes that we are wanting villain to make. Villain can have a worse hand, yet be getting the proper odds to call, thus calling isn't a mistake for him, whereby folding is.

Example: The A8s sample. If say villain has JdTd on the flop of 2c4h7d, and we have As8s, then villain has ~29% equity. If we bet 1/2 pot here, he only needs 25% equity to call. Thus he has enough equity to call correctly. Therefore, a fold from him would be incorrect. Here he has a worse hand (A8 > JT), however, we would rather him fold (I think) due to the fact he has the equity needed to call a 1/2 PSBet. That is we would rather him fold if 1/2 pot was our bet amount. If we bet larger, and the needed equity exceeds his equity in the pot, then we would want him to call.

But tbh, this is just late night ramblings, so I'm not sure it makes sense, or if it's correct. On top of all that, I'm not sure it has anything to do with the actual situation of whether we should be in these situations or not.