As a hiring manager, if I was on the fence, knowing someone I'm not thrilled with has an offer makes me try to figure out what I/we missed and I would reexamine potential gaps in our recruiting processes with the candidate, which are always wrought with biases. And luck is such a big factor (on both the company- and candidate-side) in getting a positive signal.
As a hiring manager with over two decades experience I tend not to think this way unless I know who the other hiring manager is, have reason to believe that they are strong at hiring, and that the role they are hiring for is similar enough to mine for it to mean something.
That's not to say I don't think about where I might have blind spots for a candidate—as you say, all processes are biased—but I've seen too many bozos in this industry (especially as the money started to become its own draw) to take a random offer as signal for anything. More context is necessary or it's just garbage in garbage out.