The phrase "asserting that they do" is correct and usable in written English.
It can be used when discussing someone's claim or statement about a particular action or belief they hold.
Example: "The researchers presented their findings, asserting that they do have a significant impact on the environment."
Alternatives: "claiming that they do" or "stating that they do".
But G.M. officials have said they will need to restart those plants only if market demand is sufficient, asserting that they do not need additional capacity yet.
"The president made the allegation during his opening remarks at a U.N. Security Council meeting on nonproliferation, asserting that... 'They do not want me or us to win because I am the first president to ever challenge China on trade, and we are winning on trade — we are winning on every level.' " The Chinese government pushed back on the accusation.
Some are permanently pissed, asserting that they don't and won't hire a mother so long as an equally qualified male candidate also applies for the job.
The vendors shrugged when asked how the books were produced, several of them asserting that they did not speak English.
The releases are usually governed by a 1990 law, the Older Workers Benefit Protection Act, which was the response by Congress to a rising number of lawsuits filed by older workers asserting that they did not receive the same severance packages as their younger colleagues, who were given incentives to quit early.
Christie stood by Baroni and Wildstein, characterizing the incident as a "mistake" and asserting that they did not have malicious motives and did not do it for political reasons.
Analysts and fund managers assert that they do not pick stocks based solely on expectations of foreign-exchange movements.
This is the beauty of the fictionalists' view: they endorse all of the Platonists' arguments that mathematics is best interpreted as being about abstract objects, and then they simply assert that they do not believe in abstract objects.
