Byrne was speaking to HR magazine after the lawyer, Liz Dux, who is representing over 50 of Jimmy Savile's sex abuse victims this week said they will seek compensation from the BBC, NHS, Savile's estate and other organisations.
The full scale of the late DJ's 54-year campaign of abuse was revealed in a report earlier this week.
Branded one of the UK's most prolific known sexual predators, Savile now has 214 criminal offences, spanning the breadth of the UK, recorded against his name - including 34 rapes. The BBC are among a number of organisations embroiled in the scandal and, alongside the late star's estate, could now face substantial payouts.
Byrne said: "On the face of it, the evidence seems to be stacking up that the BBC and the various hospitals that Savile worked at, were aware of the suspicions, and failed to act on rumours. These organisations owe a duty of care towards patients and guests that visit their premises.
"It does not matter that Savile was not employed by the organisation."
Byrne added: "In the case of the BBC where he abused people through his connection with programmes, then because of the close connection with the BBC, it could potentially be held to be vicariously liable in those circumstances, as Savile was acting as their agent.
"Likewise in the hospitals, he may not have been paid by the hospital but he's there as their agent, then they owe a duty of care to those he abused."
A total of 450 people have come forward alleging sexual abuse against Savile since October 2012.
Dux said all her clients were suing Savile's estate and would also pursue claims against the organisations responsible for where the abuse took place.
