My experience tutoring at university would beg to differ. Perhaps irremediably bad is not the right word, but as a tutor of ~30 first year students you find yourself almost having to give up on half the class.
I TA'd Intro to Computer Science (Java Programming) at UCSC for 2 years and I would emphatically disagree with you. The whole time I was tutoring (groups and one on one) I never met anyone who I thought couldn't learn to program. It was 100% a function of time. Some people certainly got it quicker, but I never met anyone who couldn't get it at all given they put in the time. I probably worked with over 200 students indirectly and 50 one on one and I never felt I had to 'give up' on any of them. In fact it was one of the most enjoyable and rewarding jobs I've had.
One of the problems I have with formal education is that nobody has ever considered how to motivate students. As you say, most subjects really are a function of time and effort. Even with serious roadblocks, a good tutor should be able to teach you if you spend the time. The only place where you can't teach someone is where there are discoveries to be made.
I guess I could’ve phrased it more carefully. Sure, I think everybody can learn to program, but given the limited amount of time you can spend with each student and their predisposition toward some of the key elements of programming it's just unlikely that you can teach 30 first years how to legitimately program given just a 2 hour lab each week. Keep in mind some of the students are just 'tasting' programming and some students have ridiculous external commitments too.
I tutor people 1 on 1 now, besides working, and it's incredibly better. Never in this scenario have I met anybody who's never had those 'aha' moments.