My evidence is anecdotal: I have observed many grad students in Tier-I schools come from Tier-II undergrad backgrounds. A determined search could probably verify this by looking through a bunch of online grad student biographies.

I don't think a person who is smart and disciplined enough to get into a Tier-I school, but instead goes to Tier-II school for undergrad, will suffer a big penalty in terms of acceptance chances at Tier-I grad schools. Not because the admissions people don't take the prestige of the undergrad university into account; they surely do. But a Tier-I capable individual at a Tier-II school will receive a lot of counterbalancing benefits as a result of standing out relative to his/her peers. Such a student will probably get better grades, and receive more positive attention from professors, including letters of recommendation and summer research opportunities.