Here is a fundamental way HR can affect hiring:
Do you have a low credit score (maybe through no fault of your own, e.g. medical bills)? Do you have a "checkered" past -- maybe many years distant, now, with a solid track record in between?
Do you not test as "mainstream" on psychological evaluations?
These are all things that can stop you from getting to the next step in the hiring process, at an established company implementing the ever vaunted "best practices". (Which, when widely followed, can really only ever be the "standard" (some might say, mediocre) practices.)
HR doesn't evaluate your true professionalism. They just make sure you don't deviate too far from standard.
One reason actual teams and hiring managers sometimes have to put significant effort into fighting their own HR. Or deciding whether doing so is worth the risk to their own jobs and standing.
P.S. Yes, I'm pretty cynical about HR -- the result of long experience.
This month, I've watch HR at another large, established institution (this one focused on healthcare) take the easy way out of letting a supervisor and her favored push out a better employee, instead of investigating what's really going on (which, given the nature of the job and all the client interfacing and record-keeping, wouldn't be that hard to do).
HR there appears to actually have started picking up on what's happening (truly abusive behavior by this supervisor and her cronies, lying, and borderline neglect of their own jobs -- foisting their duties onto the underdog employees). Nonetheless, it's easier to accept a forced resignation than to try to address the team problem. Which will fester until something really goes wrong.
Or, if HR there is good at its job, within the scope of what they're willing to do, until they can build enough of a case/impetus against this supervisor to force her out, on their terms and timeline.
Even if they do that, they've let at least two of their best employees get screwed over, in the meantime. Go, HR! /s
As always, as an employee, HR IS NOT YOUR FRIEND. They take care of themselves, and the institution. You only win if it's the easy win, for them. Or with lawyers.