OK. But that seems to me to be overly vindictive. After all the whole idea of prison is to serve your time and be returned to society. I don't agree that any organisation could or should refuse to employ anyone who has been convicted of a crime. That is not a socially healthy system.
I don't think that the BBC as public broadcasting company should have different morals/behaviours to the rest of society. So one part of your assertion is obviously the right thing and the other is equally obviously wrong:
Acting against Paul Gambaccini and not acting against Savile are two sides of the same, wholly abhorrent coin and the BBC must be brought to book for both of those behaviours.
Acting against people with criminal records, who have served their sentences is not what the wider society should do, it is overly punitive. So, given that there will always be exceptions to that rule, I don't agree that Boy George, Ashley Blake, Jonny Dymond, David Dickenson and, probably, countless others should be barred from working for the BBC.