Yours and @x2boys ' innocence was exactly what used.
"Look at me! I'm just so much fun and so quirky!" All of those poor children - boys and girls - predated by this vile man.
Some people are blaming the fact that his mother didn't love him. Lots of children aren't loved. Lots (in that era particularly) were beaten. People believed that to spare the rod was to spoil the child. It didn't turn them all into cruel, heartless perverts.
I think she found him hard work - she had six other children, and he came along later in life, and the family - like many at the time - was very short of money. Life was hard for all working people then. There was a depression which got worse and worse, effectively until the war started in 1939 (and of course there was further privation afterwards). I'm sure that he suffered want - almost everyone did. He was born the year after my dad, in a similar working class pit town. According to Wikipedia, he left school at 14, and got an office job. My dad left school at 14 and went into the merchant navy. Savile was sent down the mines when he was 18 - my dad had been on ships which were protecting convoys from being 15 years old. My paternal grandfather had abandoned the family when my dad and his brother were still infants, so their mother really struggled in those days before the welfare state - would have had much less money than the Savile family. I just mention this to show that Savile might have had it hard, but he didn't have it any harder than most, and cushier than some.
"The Duchess" was probably exhausted and worried sick about making ends meet - I daresay she was short-tempered. Did she love him enough? She loved him enough to pray for his recovery when he was seriously ill as an infant. Women then weren't as "huggy" on the whole as women are now. They didn't have time to sit and indulge their children. Every meal had to be made from scratch; all washing was done by hand, or in a big copper boiler using a washboard; all dishes washed by hand; most children's and women's clothes hand made - and this was a family of seven. I doubt she had the time or energy to sit and read with him, play with him etc - it doesn't mean she didn't care for him.
One of his older brothers was also a sexual offender. Nature or nurture? Both, I would think, though I think it's unfair to put all of the blame onto his mother. He had a father, too, remember, and 6 older siblings (2 brothers, 4 sisters). Any and all of them could have contributed to his nature. Or he could just have been born nasty. Pity nobody ever got to speak to any of his classmates, old girlfriends, schoolteachers etc.
Edit: Grammar