The phrase "asserted that only the" is correct and usable in written English.
It can be used when introducing a statement or claim that emphasizes exclusivity or limitation regarding a subject.
Example: "The researcher asserted that only the most relevant data would be included in the final report."
Alternatives: "claimed that solely the" or "stated that just the".
He asserted that only the originalist position, as opposed to the view that the meaning of the Constitution may change over time, was legitimate.
The Justice Department had asserted that only the boy's father, and not his Miami relatives, was legally entitled to speak or him, since a child could not comprehend the complexities of an asylum claim.
In a 1967 book, "Man in the Trap," Baker asserted that "only the most hideous distortions of orgonomic truth" could cause a person to equate Reich's "work, thinking, and hopes for mankind with those of present day liberals, leftists, and beatnik-bohemians who have in one way or another attempted to identify themselves with orgonomy".
The vendors confronted witnesses who provided evidence of trademark violations and filed a countersuit asserting that only the government can shutter a business.
It was, in a legal sense, only a ruling on an emergency injunction to keep the child in this country for a few more weeks, but the language seemed to chastise the government for asserting that only the boy's father was legally entitled to speak for him.
Conrad asserts that only the latter attitude can reveal the "ideal Object" that is the genuine or intended [gemeinte] work of art.
The Chinese government in 2007 passed a law - apparently without irony - asserting that only the atheist Chinese state can appoint the religious leaders of Tibet.
The president's sanguine outlook, however, seemed at odds with a Pentagon report issued in December, which asserted that only one of the Afghan National Army's 23 brigades was able to operate independently without air or other military support from the United States and NATO partners.
Morgan accused Gaga of creating her diagnosis "for attention" and asserted that only people in the military can have PTSD.
Mead [ 19] has asserted that only by involving women in the planning for services will you gain their engagement.
Therefore, to assert that only those without children vote against the budget makes no sense to me.
