"quite contrary to" is correct and usable in written English.
You can use it when you want to express opposition or contrast between two things. For example, "His actions were quite contrary to his words."
In retrospect, that was foolish and quite contrary to the axiom of Stanford Athletics.
This property was quite contrary to the cases of known chemical catalysts.
Disruptive business events may occur that are quite contrary to what the senior management expected.
Shortages forced farmers off the land, quite contrary to de Valera's philosophy.
But a fatwa on never entering government again would be quite contrary to what liberals believe.
His dreamy work pursues goals quite contrary to the constant concern for reality that characterised both Monet and Degas.
It is evidently agitation of terrorism quite contrary to the purpose and nature of the Berlin International Film Festival".
Thus, in the end, I found out the hard way that Mr Magoo, quite contrary to its self-serving disclaimer, is a completely accurate portrayal of poor eyesight.
"There is quite a lot of payment by local authorities for payment by the minute, which is quite contrary to the wellbeing principle of the Care Act.
One of Crescas's main works, Or Adonai ("The Light of the Lord"), was quite contrary to Gersonides in its attempt to expose the weaknesses of Aristotelian philosophy.
John Russell's article about Thomas N. Armstrong 3d [ Adding Up the Costs of Changes at the Top," March 18] contains several references to the National Academy of Design that are quite contrary to fact.
