Well, hopefully, yours is one of the unusual cases where it does, because if they don't discount the quality of your site but rather allow the 'thinning' of PageRank passed, visitor behavior and 'other secondary/indirect signals' to indicate your site is 'not a good choice' because of the broken links you have, it could definitely be more difficult to overcome.
In other words: People with broken links, especially ones that frustrate visitors when they find them and click, may have a much bigger battle to getting their site back where it was.
Them 'not discounting' a site with broken links on it is not necessarily a good thing, in fact, it could range from 'bad' to 'really really bad' for sites with broken links in many cases, because 'just fixing the links' may not solve the problems created by other signals sent and directly used for ranking purposes.
There are actually a bunch of possibilities for 'influence' on rankings from broken links he doesn't specifically address, and I wouldn't expect him or anyone to sit and explain all of them to you, one, because there are a bunch, and two, because if it's someone from Google, they could easily 'give away too much' by listing everything that Could be influenced and how.
I'm really not sure I understand the point of all this...
We're talking to you from years of experience and knowledge, not 'just making things up' or trying to 'lead you down the wrong road', but if you really believe broken links will not harm your rankings, whether directly or indirectly through other 'signals' and 'factors', then leave them broken.
There's no way I'm going to go into exactly how and all the different ways broken links can influence your rankings, because, quite frankly, you're not paying me anywhere near enough and I have other things to do.