Adams and other former BBC executives, including ex-director general Mark Thompson, were yesterday grilled by a cross-party group of MPs, led by Margaret Hodge.
The BBC has come under fire for paying more than £25 million to 150 outgoing executives between 2009 and 2012, which included £2 million more than they were entitled to.
One of the members of PAC, Stephen Barclay, asked Adams if she had been giving instructions to HR staff that they should be lax about payments made to out-going staff because they should view it as sweeteners.
Adams said that she could not "honestly recall using the word sweetener".
Barclay then read an email sent by Adams, which he had received from a whistleblower, in which she used the term.
Adams replied: "HR professionals all over the world recognise that occasionally you have to pay above contractual entitlement… I may have used the term by means of an incentive to get to a swift resolution."
Barclay added: "It says something about the culture that public money is bandied around particularly at a more senior level and then the head of HR is saying to use licence fee payers' money as sweeteners."
Adams, who stepped down last week from her £320,000 a year job, told the committee the corporation was trying to "get people out of the door" with minimal disruption and no risk of legal action so it was "occasionally" necessary to pay more than was contractually required.
Responding to this, Hodge said: "This attitude that the top cadre of people at the BBC faced greater difficulty when they faced redundancy rather than a receptionist or someone lower down is offensive, just offensive."
Excessive redundancy packages
During three hours of questioning yesterday by MPs, Thompson and Lord Patten, accused each other of paying excessive redundancy packages funded by the licence fee.
Thompson said the move, which saw former director general of the BBC Mark Byford leave the BBC with a payout of £949,000, represented "value for money".
He said the pay-off was part of a move to axe senior executives which would give the BBC "£19m of savings for every year into the future" and he believed he "had the full support of the BBC Trust" to order it.
At the end of the three-hour hearing the committee's chairman, Margaret Hodge, told the BBC: "At best what we've seen is incompetence, lack of central control, a failure to communicate for a broadcaster whose job is communicating.
"At worst we may have seen people covering their backs by being less than open. That is not good."
She added that the meeting was an "unedifying occasion, which can only damage the standing and the reputation of the BBC".
The BBC has now introduced a £150,000 cap on severance payments.
BBC's top severance payments:
Mark Byford, deputy director general, 31 years of service - £949,000
Jana Bennett, executive director, 33 years - £687,333
Caroline Thomson, chief operating officer, 17 years - £680,400
George Entwistle, director general, 23 years - £470,300
Roly Keating, departmental director, 29 years - £376,000 (money returned minus tax)