"challenges the assertion" is a correct and usable phrase in written English.
You can use it when someone is questioning or disagreeing with a statement or claim that has been made. Example: The scientist's research challenges the assertion that global warming is solely caused by human activity.
In his book "Poetics of Music," Stravinsky challenges the assertion that the early Verdi works, steeped in the traditions of Italian opera and thick with oom-pah-pah arias, are somehow negligible, and that only with the more experimental operas of his later years did Verdi reach his potential.
Polysemy challenges the assertion that the "intended" meaning of the Laozi can be recovered fully.
Peter Hunter challenges the assertion by mediaeval sources that spoke of Felix and Sigeberht travelling together from Francia to England, as in his view Bede's Ecclesiastical History of the English People implied that Felix went to East Anglia because of Honorius at Canterbury.
Moreover, the high retention in HCU-trained community health workers challenges the assertion that non-financial incentives are insufficient to retain community health workers (Walt et al. 1989; WHO et al. 2008), since HCU does not provide significant salaries.
Our finding that beta-cell dysfunction is present in a subset of critically ill children with CIH challenges the assertion from adult studies that CIH is primarily the result of elevated insulin resistance.
The report also challenges the assertions of Boris Johnson and his more bumptious media chums that early predictions of substantial numbers of claimant households having to move were baseless.
He urged students to "challenge the assertion," a catchphrase that would resonate with a generation of young officers.
Colin Montgomery Edinburgh I challenge the assertion that Beppe Grillo's Five Star Movement poses an alternative to the dogma of austerity.
A historian outside the Howard group has even challenged the assertion that the "sankofa" sign had the African meaning ascribed to it.
I feel I have to challenge the assertion one Momentum attendee made to Paul Mason, namely that "the whole city's buzzing".
They also begin to challenge the assertion that men are the most likely victims; violent crime against men continues to fall.
