I would agree that connections play a large role in the application process. I know of (many) successful applicants in the past/current cycle who did not have 20 pubs, subpar GPAs, etc, but have given their soul to well-established POIs in the field for the past however many years prior to applying.
i think ultimately as a POI, it is very difficult to pick a grad student from hundreds of deeply committed/passionate and, if I may say, overqualified candidates. Even if someone looks AMAZING on paper and the credentials are second to none, he/she may still be a psychopath who you won't want to deal with for the next 5 years. So ultimately you fall on the LOR assessments and if that LOR writer is someone that you already know and whose opinion you deeply respect, then clearly you are more likely to judge this candidate favorably.