The phrase "asserts only that" is correct and usable in written English.
You can use it when you want to indicate that a statement or claim is limited to a specific assertion without making broader implications.
Example: "The author asserts only that the findings are preliminary and require further investigation."
Alternatives: "claims merely that" or "states solely that".
Under the law, officials have to assert only that foreign intelligence is a part of their need; before that, it had to be the only purpose.
Under the Patriot Act, the F.B.I. must assert only that the records gathered through the letter are considered relevant to a terrorism investigation.
The statement, written by the university's general counsel, did not explicitly deny that the school discriminates against Asian-American applicants, asserting only that its practice of "considering race" is "fully compliant with the law".
As for the White House, officials will assert only that the president never saw the Mychal Judge law as a gay issue, and that the brief e-mail announcing its enactment was business as usual.
Red Bull, which was founded in 1984 and has a dominating 40 percent of the energy drink market, did not comment on the Drink Water campaign specifically, asserting only that athletes should combine plenty of water with physical activity and energy drinks.
"Some works became cultural-affirmation images, asserting only that we exist as distinct cultures," explains Baca.
The outcome was Verificationism, a view which asserts only the statements that are empirically verifiable are cognitively meaningful; in other words, statements or philosophical propositions must be either true (verifiable) or false (falsifiable); otherwise they are meaningless and nonscientific.
According to Grice's account, the speaker doesn't assert, only implicates that the events took place in the order recounted.
This doctrine is important because a bankruptcy trustee can assert only those claims that the bankrupt company could, and if there would be a valid in pari delicto claim against the company, then it can be asserted against the trustee.
