In the case of ThingShare, what are your big assumptions that are core to your business working? I would say it's not whether people will list their games online, that's trivial and not really required by the product. It's not whether people want to rent games, that's proven.
I think your two biggest leaps of faith are (a), that people are willing to lend their expensive games to a stranger for a small sum, and (b), that people will be reliable about sending their games to other if your product works by mail or if it works locally, that they will be willing to meet a stranger in person to exchange.
To test those assumptions you don't build a broken website and automation system. You have a web form, using Wufoo or Google Docs. Have people list the games they want to rent and the games they want to lend. Then you search the database/spreadsheet, make matches, and make all the arrangements. Make pre-paid mailing labels, give them directions to where they are going. Do everything, just do it all manually, you only have 30 customers.
In the match.com example, you don't build the next match.com. That is, you don't build a whole site with a bad UI/UX. By saying you want to build the next match.com you are really saying that match.com is doing something wrong, and you can do better. What is it you can do better? What is your assumption?
I don't know match.com, so I'm making this up. Maybe your big assumption is that the reason match.com doesn't work is because it doesn't take into account financial parity. So you offer a service that will match people up with others that make the same amount of money. No algorithms, you may not even need a website, just match people up. If that works, if people go for it, if they like their dates, test your next big leap of faith (maybe that people won't lie about the income?).
No, Lean Startup focuses more on multiple iterations, aka MVPs. Test the next feature, the next function. This is what ThingShare has been doing all along, while still completing shares.
What people have assumed is that we didn't complete the process, where the website failed to complete the task we took over manually. It worked well, but users were still disappointed by the site (not by us).
Oh, and we have significantly more than 30 users, that was a point in time with a very early iteration.
"Every business plan begins with a set of assumptions. [...] Because those assumptions haven't been proved to be true (they are assumptions, after all) and in fact are often erroneous, the goal of a startup's early efforts should be to test them as quickly as possible." - The Lean Startup, page 81
"Unlike a prototype or concept test, an MVP is designed not just to answer product design or technical questions. Its goal is to test fundamental business hypotheses." - The Lean Startup, page 93