The Tory Home Secretary was not asked about the decision to place Liberal Democrat MP Norman Baker in the Home Office, it is understood.
Mr Baker claims in a book he authored that scientist David Kelly, who leaked information on the investigation into Saddam Hussein's so-called Weapons of Mass Destruction to BBC journalist Andrew Gilligan, was murdered in 2003 after he was found dead in a field near his home. It alleged security services staged a cover-up at the height of a controversy over claims the last Labour government "sexed up" a dossier which helped build the case for the Iraq war.
No 10 sources said the decision was signed off by the Prime Minister David Cameron.
But they refused to be drawn on whether the Conservative leader had the power to veto an appointment seen as in the gift of Liberal Democrat leader and Deputy Prime Minster Nick Clegg.
The appointment came as Mr Cameron chose not to change any cabinet ministers but handed promotions to women including Esther McVey, the former GMTV presenter who was pushed up the ranks at the Department for Work and Pensions to become employment minister. Anna Soubry was moved from her role in the Department of Health to become the first female MP to be a minister at the Ministry of Defence.
Allies of Chancellor George Osborne also fared well, with Sajid Javid made Financial Secretary to the Treasury, Matthew Hancock becoming Skills and Enterprise minister and Greg Clark installed as Tory Deputy Chief Whip. Andrew Robathan was made Northern Ireland minister replacing Mike Penning, who takes on duties at the Department for Work and Pensions.
Hugh Robertson, who was widely praised for his work on the Olympics, is rewarded by being made minister at the Foreign Office. Mr Cameron's parliamentary aide, Sam Gyimah, has been moved to the whips office.
Tories who lost their roles included Mark Hoban, Mark Prisk, Richard Benyon and Alistair Burt.