I doubt very much that "complex" was meant as an indicator of 'sleeping with women'.
Whether that was code for 'oh, we daren't tell her the real truth' or whether it is simply indicative of one explanation she was given by senior civil servants (there were four rebuttals, apparently) is obviously unclear.
I would, however, very much doubt that there was a tendency of rejecting anyone (male, certainly) for a gong on the basis of heterosexual promiscuity. After all, the English upper classes have hardly been paragons of abstinence and monogamy - or even heterosexual exploring a, if we take into account public schools etc.
I doubt that Mrs T herself was particularly naive.
It has been pointed out a number of times that for someone to have spent so many holidays at Chequers, he must have been vetted by the security services. His own 1974 autobiography made entirely clear that he was abusing his position for sex (and that he was not arrested because the polices were doing the same).
The mainstream media knew - and chose to nothing.
Now, Jerry has previously made some excellent comments on the change in culture in this respect, and I think he's essentially correct.
The point is that the BBC has been made a scapegoat - largely for reason of political agenda - but it is increasingly clear that a great many people, including some in positions of great influence, knew that Savile was "complex", and did nothing. The point is not that 'Thatcher was to blame', or anything as crass as that, but that people in very senior positions knew that something was amiss. And goodness, it's fairly widespread knowledge that Phil the Greek worked his way through the lady's maids and that Andy is not exactly 100% hetero. So again I'd suggest that, unless the 1980s were a sudden time of sexual Puritanism, it was not about consensual sex between adults.