I do not think it's the case that Minnesota offers top methods training. Certainly not compared to either of the other two schools this person is considering. John Freeman (who is admittedly very good) is the only legitimate quantitative methodology faculty member (and maybe Shawn Treier, but junior faculty probably shouldn't count). The rest of the people they list under "methodology" on their website are simply scholars who do some quantitative work, not people doing original research in methods. This is an important distinction, even if it is not your intention to do such work.
At OSU and WashU, on the other hand, you can learn methods from people who are doing methods research. Of those two, WashU edges out UIUC in terms of placement, although either place is going to be decent place for studying behavior. WUSTL appears to have placed American Politics people this year at Yale, UTD, Colorado, George Washington, and Georgia State, a very good placement record for one year, and this was a particularly bad market. University of Illinois does not have a comparable record, even in a year with a good market.