The phrase "asserting correctly" is correct and usable in written English.
It can be used when discussing the act of making a statement or claim that is accurate or true.
Example: "In the debate, she was asserting correctly that climate change is a pressing issue that needs immediate attention."
Alternatives: "stating accurately" or "claiming rightly".
During campaign stops in Florida and Oregon this week, Mr. Gore has asserted, correctly, that many drug companies spend more on marketing than research.
Alan Rutkin Great Neck, N.Y., Nov. 11, 2008 To the Editor: William Kristol asserts correctly that Barack Obama's Fido gambit showed his human warmth and bonded him to dog lovers, the allergic and compassionate saviors of mutts in shelters.
He asserted correctly that "conjectures are of great importance since they suggest useful lines of research".
So, for example, □~□⊥ makes the dubious claim that PA is able to prove its own consistency, and ~□⊥ → ~□~□⊥ asserts (correctly as Gödel proved) that if PA is consistent then PA is unable to prove its own consistency.
A Pentagon official asserted, correctly, that in the Vanity Fair interview Wolfowitz "made clear that there were multiple reasons for the use of military forces against Iraq".
The site calls call the director of the Connecticut ALCU "an asshole" in a piece about the Bridgeport shooting, though they do assert correctly hat we don't fully know what happened yet.
Moreover, the penmen of the established order, the state and the business world are endeavouring to tempt him into a moderate course by asserting (perhaps correctly) that the epithet "Islamist" does not become him.
The presenters assert, probably correctly, that the Spanish song repertory is the most overlooked among singers, both professionals and students.
In all the publicity, there have been no reliable statistics as to how many British teen-agers are using drugs of even the milder sort, and some calm voices assert probably correctly, that the number is minuscule.
