> there was a breakdown in internal communication where HR was under the impression we wanted to hire at any cost despite us giving the candidate a mediocre rating
If HR hired the person despite a mediocre rating then they're the ones that need to be sacked.
Quality is a process that begins with management. How they value it is revealed by the actions they take in cases like these.
It's unfortunate OP wrote plenty about their displeasure with the candidate but failed to tell us anything about their role in the hiring process, how well the job description matched the actual job requirements or how HR got the impression it did.
But the situation as described strikes at a reason I've left previous jobs: the feeling that I couldn't trust the competency and integrity of those I worked with.
Like the time our in-house recruiter presented me "resumes" they fabricated from linked-in profiles of people they wanted me to interview but who hadn't actually applied to our company, or the time I was pressured give passing reviews to candidates who couldn't pass basic programming tests from managers eager to hire loyal toadies.
A small outfit with a focus on personal development, intrinsic motivation, good climate, and low turnover can't afford incompetent or perversely motivated HR people who "hire at any cost" candidates with mediocre reviews.
If HR hired the person despite a mediocre rating then they're the ones that need to be sacked.