Yeah, I have no idea what they're talking about with that one. I've caught bugs when reviewing code without needing to run it before, and I've had the same happen to me in reverse, and I've seen it happen between others on reviews I was observing. I guess they could find some way to define "in general" so that this is technically true, but at that point it's not particularly meaningful.
Arguably, if you can’t tell if the code will halt, the code is not acceptable. Code is acceptable if it can be properly reasoned about. If it can’t, it is not.
Yeah, this seems like a misunderstanding of the halting problem. You can prove that a program halts will halt; you just can't prove that it won't halt if it doesn't.
