The phrase "avowed that" is correct and usable in written English.
It can be used when someone is declaring or affirming something openly and publicly.
Example: "She avowed that she would never return to that place again."
Alternatives: "declared that" or "asserted that".
And, even more strikingly, Pérez Molina avowed that he did not personally know Captain Byron Lima.
Avital Leibovich, avowed that "anything affiliated with Hamas is a legitimate target".
By Jill Lepore Bradley avowed that his game would promote virtue.
For the first time ever, the security services have avowed that they do monitor communications in bulk".
Kaiser Chiefs never hid behind false morals where ambition was concerned; singer Ricky Wilson once memorably avowed that he would "wank off a tramp for success".
In an editorial in the magazine, the staff avowed that capturing the event in pictures and writing was a responsibility that would commit the events to shared memory.
(She avows that history has taught nothing to Germany's leaders if they think it possible to kill ideas).
He does not hesitate to avow that much of what he is and does, "even my way of being an atheist," bears the imprint of the Roman Catholicism to which he adhered through adolescence.
"No one who lives in the city would avow that problems don't exist, but cockroaches are not among them," said Luigi Savastan, a newspaper vendor on the Via Chiaia, citing the city's high unemployment figures that serve to swell the ranks of Naples's notorious organized crime families.
Within a month, female celebrities were going on TV to discuss their problematic BRF; websites were helpfully naming other celebrities with BRF such as Kristen Stewart and Charlize Theron; plastic surgeons avowing that, indeed, BRF is a "definite phenomenon" and they can offer "expression surgeries" to ameliorate the problem; magazines warned female readers about the likelihood that they have it.
Here's an analogy: Would it be fair to install the same number of bathroom facilities for men and women in public areas, when all of us can avow that most of the time the women's bathroom has the longer line?
