There is still a bias but not as stark. The last institution typically gets the most weight, and research becomes a much bigger factor. At my med school's IM program (lowish tier uni), the Carribs were still at a significant disadvantage for competitive fellowships vs US MD, in terms of # of interviews and match-rate. DOs had it harder than USMD but not as bad as Carribs. If an elite DO makes it into a strong IM program, they shouldn't have any issues. Interestingly, last year there were several DOs and Carribs who made it into Penn IM through Drexel's disbanding, but their match wasn't "Penn caliber". That may have been moreso because they were at Drexel for most of their training, as the typical Penn resident who does 1 poster will still get tons of top interviews.
Re: prestige, it definitely isn't everything, but it's more about opening options at every level, including mid-tiers/location. No one has go to MGH IM, but when it's more likely for a US-MD to get top 20 IM with a 230s than a DO with 250+ to get into a good mid-tier willing to take DOs like UCSD IM (1 DO from a CA program got into here last year, none this year), that is a major discrepancy. And many times we're referencing the superstar DOs who manage to get stellar scores/research when talking about options, but there are plenty who are avg/below avg - USMDs still get a ton of great options at this level.