The young person at the centre of the BBC controversy said "nothing inappropriate or unlawful" took place between them and the presenter.
A male member of BBC staff has been suspended following claims that he paid a young person around £35,000 over three years, from the age of 17, for explicit images.
The lawyer of the young person's family said in a letter reported by BBC News At Six: "For the avoidance of doubt, nothing inappropriate or unlawful has taken place between our client and the BBC personality and the allegations reported in the Sun newspaper are 'rubbish'."
The Sun reported earlier today the presenter had made "panicked" calls to the person last week after the allegations became known.
A spokesperson for The Sun told the BBC: "We have reported a story about two very concerned parents who made a complaint to the BBC about the behaviour of a presenter and the welfare of their child.
"Their complaint was not acted upon by the BBC. We have seen evidence that supports their concerns. It's now for the BBC to properly investigate."
The BBC said it had been investigating a complaint since May, and that new claims of a "different nature" were brought to it on Thursday.
As well as being in touch with the police, the corporation is carrying out its own inquiries and talking to the young person's family.
BBC director-general Tim Davie is due to face the media on Tuesday for a scheduled briefing following the release of the corporation's annual report.
In a note to staff on Sunday, Davie said: "The BBC became aware of a complaint in May; the BBC investigations team have been looking into this since it was raised and have been actively following up.
"New allegations, of a different nature, were put to us on Thursday, and, in addition to our own inquiries, we have also been in touch with external authorities, in line with our protocols.
"I can also confirm that we have suspended a member of staff."
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