The Scottish Conservative leader, who is gay, plans to marry her partner in the near future.
"Folk might remember I fought a leadership election on the other side of that particular argument", she added.
The Scottish Daily Telegraph's Alan Cochrane said: "The story was impeccably sourced and I stand by every word".
Ruth Davidson has given Sinn Fein- and Jeremy Corbyn- a stick with which to beat the fledgling Conservative-DUP partnership in its infancy period.
"I think we can have a tremendous amount of leverage".More news: Apple reveals watchOS 4: Siri-powered updates, fitness syncing, and music playlists
Many commentators focused on the DUP vetoing the introduction of same-sex marriage in Northern Ireland in 2015, in opposition to the rest of the United Kingdom, and in stark contrast to this country which voted in favour of same-sex marriage in a referendum.
"I asked for a categoric assurance that if any deal or scoping deal was done with the DUP there would be absolutely no rescission of LGBTI rights in the rest of the United Kingdom, in Great Britain, and that we would use any influence that we had to advance LGBTI rights in Northern Ireland". The DUP has repeatedly blocked legalisation allowing such unions, despite a majority of assembly members supporting the move at the last vote.
Striking a noticeably more conciliatory tone than Mrs May, Ms Davidson said Labour's campaign had "struck a chord" with voters and that the Tories should seek agreement with the other parties on how best to proceed with Brexit.
"If we are going to build a society that is fair, decent and safe we have to be tolerant and fundamentally that is about individuals being able to prosper in a free society - not just financially but socially, intellectually and culturally", he said.
"The Prime Minister has made it clear it is her duty to get on with the job in hand and I support all efforts to do so", she said.More news: Ariana Grande's Manchester benefit concert goes on
It opposes same-sex marriage and is anti-abortion - with abortion remaining illegal in Northern Ireland, except in specific medical cases.
"What Theresa May must not do is allow the DUP to push her into the corner where the only way forward for her is the hard Brexit".
'One of them is country, one of the others is LGBTI rights and I asked for a categoric assurance that if any deal was done with the DUP there would be absolutely no rescinding of LGBTI rights in the rest of the United Kingdom and that we would try to use any influence that we had to advance LGBTI rights in Northern Ireland.
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