For the warm fuzzies, you're right. manual is better - but as far as actual security is concerned, manual is exactly as secure as automatic.
Your example is different than what the OP described but that doesn't change anything. Let's use your example for a minute.
In your example, PersonA sends an email to third party saying they received the goods (condition and everything) and then, based on that email, either (A) the script tells Pay Pal to deliver the money or (😎 the third party goes to Pay Pal to manually deliver the money.
You presented a threat model that, in your example, PersonB could spoof an email. But couldn't PersonB accomplish that same fraud if the funds transfer was handled manually? That is: PersonA buys from PersonB, PersonB sends a spoof email to 3rd party saying everything was delivered perfectly, 3rd party goes to Pay Pal and manually delivers the money. B closes the Pay Pal acct and disappears with the $$$. In other words, in your example, handling the transfer manually doesn't add any additional security.
The only reason that fraud is possible in your example is that payment hinges on a mere email from A saying that the product was delivered successfully. And email is horribly insecure as you easily pointed out. So in a real world product, you would never transfer funds (manually or automatically) based on words in an email. Of course, the OP wasn't suggesting that they were going to do that.
In a real world product, the 3rd party has a login screen for both buyers and sellers. The only person who can state that the product was delivered successfully is PersonA. And if the 3rd party has a login screen with a username and password, then PersonB cannot pose as PersonA to flag the transaction as complete.
So as you said, the entire process relies on verification of PersonA stating that they received the goods. But how you verify PersonA has nothing whatsoever to do with how you are going to transfer the funds later.
Transferring the funds manually adds the illusion of extra security. It's a nice warm fuzzy but it's not really even a little bit more secure. You talked about covering your butt. If fraud does get committed, what defense is the 3rd party going to use? "No no, it's not my fault. I'm not liable because I transferred the funds manually at Pay Pal." The fact that 3rd Party transferred the funds manually doesn't help cover their butt one iota. If they got tricked because they didn't do a good job of verifying (authenticating) PersonA, it's not going to matter that they transferred the funds manually - that doesn't cover their butts.
The illusion is created partially because doing it manually takes more effort - it seems to make sense: if it takes more effort, then it must be more secure, right? The truth is that the security of the entire system lies in how strong you make your web site (that is authenticate PersonA), not whether the owner of the 3rd party web site has to take an extra 20 minutes a day to process the funds transfer manually.
Transferring the funds manually or automatically are exactly equal from a security perspective.