Of my four full-time jobs in my career, one had a prior contact and one was a you-know-nothing,-you're-a-college-hire job. (Much of my consulting comes from my personal network, of course.) Two were startups, two were big companies. Interestingly, the startups were
more amenable to "you don't know this but you are obviously capable of picking this up".
Your point about personal appeal is well made, and I'm pretty good at projecting even though I pretty consciously avoid a lot of what the startup world thinks makes it great (and I won't work at one again because I respect myself). It helps that, to toot my own horn a little, I'm pretty good; I have a broad base of stuff to apply to a problem (even when I didn't know Ruby I knew Perl, Python, JavaScript, Smalltalk, Lisp...) and I can talk my way into an understanding via analogy and fundamental knowledge.
But what I think really matters on this front is that I'm able to express that I'm competent to somebody, and I don't need a whiteboard to do it, and I really do think that's key. My view of it is that all I need is to get somebody who's willing to listen and I'll pry that door wide open. I'm one of those people who interviews (well, interviewed, I like consulting) aggressively and habitually, and I have an Excel file with the results or non-results of every resume I've ever sent out in my life (155). When I look at he number of times I have gotten to at least a phone interview (112), not gotten an offer (53, but that includes me declining them), and gotten a reason why (21) that was related to a lack of direct subject matter expertise...I get a real small number. Two, as it happens. And this is totally a small sample size, I am not claiming statistical relevance. But I think the recognition that this industry, despite protestations of logic and high-mindedness, is still fundamentally and inescapably about making connections with people and making them like you, is something that even small-sample data like this can indicate. Most tech folks won't take this to heart, because of all the weird factors and weird people involved, but I do think that some pretty straightforward Dale Carnegie stuff is as beneficial to a reasonably good developer as anything they can learn with their hands on a keyboard.