Is Libertarianism anti-democratic?

I wouldn't have thought so, but in rereading an old blog post by the economist Edward Glaeser from Harvard and his description of how Libertarians would have restricted the government's response to existing tort laws deal in the case of the BP oil spill in the Gulf of Mexico:

Even more problematically, the libertarian’s solution requires us to place great trust in part of the public sector: the court system. At times, judges have been bribed; any courtroom can be influenced by the best lawyers that money can buy. Andrei Shleifer and I have argued that the early regulations were appealing precisely because of a sense that the courts couldn’t be counted upon to protect private property.

it occurred to me that it might be.  Why are the court's to be more trusted than other forms of government?  If I introspect a bit (in my youth, I registered with the Libertarian Party and continue to find some aspects of their arguments enticing), it may have more to do with personality than conscious, rational philosophy.  I wonder whether people who like clear, precise rules are more apt to take a Libertarian stand.  Of course, they will argue it's the result of rational analysis, but in the words of David Hume, "Reason is a slave to the passions."