IMHO the HR Manager has to assess this aspect in greater detail, given that he has more experience and also, perhaps, his is the final stage after which the recruitment process ends.
Of course even a less experienced recruiter may, with time, be able to recognize some non-serious candidates straight away and reject them in the first round itself.
At the same time, as already pointed out above there are many indeterminate factors in recruitment which become clear only after an offer is given since till then the Candidate is not really thinking about them. A skillful recruiter / Manager may use a " trial offer " to gauge the candidate on this aspect . And if there are skilled Consultants involved in the process they can help in many ways.
I am aware of a situation presently - senior level - where after accepting the candidate is having second thoughts . It is interesting since the Consultant who proposed him to the Company does not seem aware of this - he should have been.
Counter offers and second thoughts - particularly for middle / sr. Management positions should be expected as a norm, and planned for accordingly .
But sometimes, inspite of everyone's best intentions things may go wrong - even some months later. Here is a recent example you might have seen in the media :
Scroll.in - News. Politics. Culture.
It is best to acknowledge such errors quickly and move on - for all concerned.