This is a painful topic. To be honest about what grades mean you have to abide by the rule you announce as to what passing means. On the other hand it is hard to assign a numerical grade accurately. So in the case of near failing grades, I always looked again very closely at not only the number, but the overall impression of the performance. I also eventually developed such generous conditions, (e.g. I dropped several low scores then I gave three different grades: based on averages, including or excluding homework, then based solely on the final exam, with passing allowed for passing on any of them), that a student who did not pass based on any aspect of this offer, really should not pass.
Nonetheless I violated my own terms in favor of at least one student. This was initially a goof off who got religion when I emphasized that just being a senior with a job offer was not sufficient to get a pass, one had to earn it. The student began to work all the homework, to come into office hours regularly for help, and really improved over several weeks. There followed a decent final performance that still (this was before broadening the passing scheme) produced an average that came up only to 69.4%, when 70% was the passing minimum. I agonized and felt guilty, obviously since I still remember it, but ultimately gave it to him, but did not say I had done so, so as not to diminish the satisfaction.
On this topic you might read the life story of successful author Jesse Stuart, who was failed in a college course at Vanderbilt, even though he submitted a publishable novel for evaluation, but did not complete the technically required coursework. I remember my mother arguing to me that he should have passed. but I pointed out that he did not choose to do what he was told was required, even if he did something more impressive. I myself once gave a B to a brilliant "straight A" student because he did not complete the required work, although his other work was exceptional. He later became a very successful academic and even solved some rather famous problems. But at the time, I just felt it was not fair to change the criterion for an A after stating it to everyone and holding everyone else to it. You have to treat everyone the same, and you have to do what you say you will do. But the older you get the softer you get.
If you grade strictly like this however, you will probably pay for it in student evaluations, and may have trouble winning teaching awards based on them.
By the way, if you want to learn what teaching was like in the rural Kentucky schools where my father grew up, read Stuart's "The thread that runs so true", wherein he describes having to literally fist fight recalcitrant students, as well as their parents who wanted to break up school functions. He even walked over a snowy mountain pass in winter, sleeping under a makeshift cover, in order to bring back books for his students.
One father came by the school to complain that his son was attending school rather than working the family trade. Stuart took a look at his wagon load of coal, and taught him to compute its volume, learning thereby that he had just been severely cheated by the coal buyer. The father allowed the son to remain in school. Honest teaching is a worthwhile practice.
