*I didn't hear the speech, and I didn't look for a transcript, so I don't know if Small's paraphrase is accurate. The point, however, is to examine a specific argument, not to try to discredit any individual for making it. I just want to show that I'm not making up the argument out of thin air.
The argument is actually form of a common religious argument: without God, you have no reason to be "moral", therefore you should believe in God so you have a reason to be moral. The argument fails because if you are not already "moral", you need no reason to be so, and the argument is unpersuasive; if you are already moral but don't believe God exists, then, if you are rational, you already have a reason to be moral, and the premise is trivially false. (If you're irrational, rational argument will be unpersuasive.)
The implied argument against democracy above similarly fails. If the majority of the people believe it is acceptable in general to vote on whether individuals should be boiled in oil, then the argument that democracy might lead to individuals being boiled in oil is entirely unpersuasive. On the other hand, if the majority of the people believe it is unacceptable in general to vote on boiling individuals in oil, then they know they would never vote to actually do son, and the premise is false.
This argument is in a critical family of democracy; the argument is that democracy does not find the objective truth. But this criticism makes two controversial presuppositions. The first is that democracy purports to be a method of finding the truth; the second, is that there actually is objective fundamental ethical truth to be found. Longtime readers know that I deny the second presupposition: I argue there is no such thing as objective fundamental ethical truth. On this view, democracy is a process for reconciling competing interests. There is no objective truth about what interests an individual ought to have or not have; there is only the fact of individuals' sometimes competing and sometimes harmonious interests. Democracy is simply one process among many that work to make social decisions based on these diverse interests.
It's also important to note that no one, myself included, advocates democracy divorced from any cultural or institutional framework. Democracy does not entail that every possible decision is simply put to a vote. Rather, we apply democracy at various levels of abstraction, and decisions at higher levels of abstraction are usually implemented through institutions. So, for example, although a majority of people might well vote to suppress some individual with particularly odious views, we can make a democratic decision at a higher level of abstraction to generally preserve freedom of speech, and implement that decision through the institutional framework of constitutions and courts. That we do not decide individual cases by a simple vote is not undemocratic, so long as we have democratically decided on an abstract procedure to decide individual cases.
Finally, some people do need to be "boiled in oil." Not literally, of course, but some people do need to be coerced. I've never seen any anarchist or libertarian say that all coercion needs to be unconditionally eliminated. We need to have some method of determining who gets coerced, under what circumstances, and how far they're pushed. In the end, our only choices are to make these determinations by a majority or a minority. I think I have a better chance with the majority.