The extent of that advantage is now being tested. Earlier this week, Northern Ireland Secretary James Brokenshire said that the extra £1 billion of funding for Northern Ireland negotiated by the DUP should be spent by a restored executive, something that requires a new agreement between the DUP and Sinn Fein.
This position was challenged by DUP MP Sammy Wilson as introducing an element of conditionality that was not part of the original agreement. A subsequent statement from the Conservative Party acknowledged the need for more spending even without a new executive. However, there was no similar clarification from the Northern Ireland Office.
While this may seem like double-dealing from Westminster, it reflects a distinction that was implicit in the deal that the DUP signed, particularly in the section establishing a Conservative/DUP co-ordinating Committee. It specifically states, presumably at the insistence of the Conservatives, that the Northern Ireland Secretary will not serve on the Committee.
So the DUP can fairly be said to have accepted some distance between Brokenshire and the deal at the outset, the moment of its maximum leverage.
It is worth noting that some Conservatives initially wanted to avoid a formal deal with the DUP, believing that the they would never vote to make Jeremy Corbyn Prime Minister. The decisive factor was Theresa May's need to prove to the Cabinet Office that she had a parliamentary majority in the earliest days after the election.
That consideration no longer has the same immediacy. Having pushed for the deal, the Civil Service is now probably more of a voice of caution, given the Sisyphean task of restoring devolution, a more-or-less consistent theme of Whitehall policy since 1972.
It's clear that both parties have been trying to build up their leverage. The Conservatives have been talking to the Liberal Democrats, and their have even been signs of a rapprochement between the DUP and Jeremy Corbyn's Labour. Newton Emerson has a good account of the situational logic of the latter flirtation.
The calculation that the DUP would never risk putting Jeremy Corbyn into office is nevertheless probably correct. For the most part, they are likely to be the Conservative allies that they have in truth been since at least 2015, particularly on Brexit.
They may however seek to establish their value by giving the Government the occasional bloody nose in Commons votes. The Fixed Term Parliaments Act probably gives them more scope to do this without causing an election.
Pressure to disburse Northern Ireland funding could be a key factor for division if Stormont talks do not succeed in the autumn. A restored executive would undoubtedly make delivery simpler. While the mood between the DUP and Sinn Féin is probably more businesslike than is immediately apparent, formidable obstacles remain over a range of issues including an Irish Language Act and dealing with the legacy of the past. The latter area in particular is one where many nationalists feel that a joint statement by Conservatives and the DUP has made agreement more difficult.
Update 23 July: Owen Smith's challenge to the Government today over the application of the Universal Credit 'rape clause' in Northern Ireland could be an opportunity for the DUP if it does want to give the Conservatives a bloody nose.