Actually Buffet is talking about investing in an index fund VS investing on the advice of an investment professional. He is referring to the same biases of professional investment advisers that the previous poster was referring to. Basically ordinary investors do have an asymmetric advantage over investment advisers and 'professionals'.

Hence, it may not be your intention, but you are using Buffet's quote to make the exact opposite point of what Buffet himself originally intended. And he has often spoken on this subject. See also Mohnish Pabrai and his book 'The Dhandho Investor'.