If you have to ask then you're either considering or attending a low-tier school.
I could care less about prestige but most of this information is not very good.
Everyone wants to believe they can go to a school not in the Top 40/25/10 - pick your cut-off, and still land that top 3 residency in that surgical sub-specialty or whatever, but let's be honest, top residency programs pick students from top schools to interview 90% of the time... so yes, you could win the lottery to if you buy a ticket tomorrow but saying something is possible doesn't really mean much.
Again, wishful thinking. Talk to people who have actually interviewed in competitive fields + competitive spots... they literally can chose from ANY board scores and ANY whatever (picture 500 applications with only 50 interviews)... So yes, maybe a handful of those people went to Low-tier State U, but you can bet that almost all of them are name brand approved.
I know everyone thinks they are a special little snowflake and they will be that one who slips through the cracks... time will tell.
PD's are obsessed with prestige just like you guys are. "I want to match at MGH...." well, they want someone who went to Harvard to match with them. It's kind of ironic that those who go to low-tier U don't want to match at low-tier U because it's low-tier U, but they don't
want the PD's to think like they do (discriminating against their own institution).