However, I don't know how I'd feel about being introduced to a potential romantic interest by a female friend.
I don't claim to be an expert on dating, but I intuitively understand how social dynamics work.
There's a lot of situations in which this dynamic would work just fine.
He is right that there need to be some kind of filtering though - the problem is that the men women want to date are also the girls most likely to put up with the filters.
You don't know any women?
I think that this differs from your scenario in that Jess is vouching for a guy for basically anyone, vs. Ken asking all of his female friends if they know anyone they'd be a good match with.
That said, I don't think that matters for the site in question. I'm just not a part of their target audience. Doesn't mean their idea doesn't work for other people.
If you knew "a" girl, it doesn't necessarily mean she'd want to date you, or that you'd date her girlfriends (what if her friends were all guys?)
The idea is that you have a female to vouch for you, which is social proof.
http://www.jessmeetken.com/ is based on introductions from women to other women, which eliminated the problem that women's inboxes are filled with lots of low-quality (and occasionally vulgar) messages.