I don't think you need any more answers to the OP, so I trust he won't be mad at you. (-: But just in case it helps, I agree with Kinky, it sounds fine to me and 'reconcile' is indeed a synonym.
'Doesn't square with' is another typical collocation that's more or less the same as 'doesn't match' (reality, the facts, another claim).
Positive examples are less common, but possible.
Unfortunately the Uni Leipzig text corpus has a new interface that doesn't work at all with my browser, but here are some just off the internet:
• (headline) Suicide ruling hard to square with evidence
• (headline) Bush's rhetoric on Iraq hard to square with facts
• (headline) [State Auditor's] Statement Doesn't Square With the Facts
• (headline) Scare talk on medical device tax doesn't square with reality
• (article summary) Civil-asset forfeiture doesn't square with the Constitution
• The mayor of the appropriately-named Whitesboro, NY swears its town seal is not racist--which is a bit hard to square with the seal's depiction of what appears to be ...
• Barriers to the Truth: The Historian's Desire for Certainty Is Hard to Square with the Fragility of Sources ...
• "It's a little hard to square with the fiscal realities"
• This outlook may seem hard to square with some economic forecasts predicting real GDP growth accelerating in the fourth quarter
• This physical evidence was hard to square with the loudly proclaimed assertions that Brown was shot in the back, or was shot with his hands up
• A. notoriously has a no-deadline mindset — he stages fashion shows as he sees fit, most of the time not at all — which was a bit hard to square with the rigid demands of the fragrance industry
• Muslim countries tend to have lower homicide rates than non-Muslim ones. That's pretty hard to square with the idea that Islam is intrinsically violent.
• Image of heavily armed Tennessee gunman doesn't square with what those who knew him saw
• Donald Trump's portrait of a border out of control doesn't square with what people see every day in and around San Diego, the nation's busiest point of entry
• The upstart's focus will be on "social impact content," which squares nicely with Starbucks's efforts to keep up a socially conscious brand.
• Each theory also squares nicely with the theoretical groundwork laid by Musser (2012) ...
• Vitter's voting record on environmental issues squares well with the wishes of the companies and industries that have largely bankrolled his campaigns
• Such a model squares well with theoreticians' best models for black holes and particle physics
• Spinoza's Ethics is based in a positive anthropology of man that squares well with ethical PR.
You all can decide on the German, but your suggestions of Übereinstimmung and Einklang seem okay to me as a non-native.
Not so sure about Hut, but maybe that's because in a similar English idiom, wearing the same hat would mean filling the same role, doing the same job, and is usually used of people rather than things.