The phrase "assert that they do" is correct and usable in written English.
It can be used when someone is stating or claiming that a particular action or belief is true.
Example: "The researchers assert that they do have sufficient evidence to support their claims."
Alternatives: "claim that they do" or "state that they do".
American officials assert that they do not have a preferred candidate for prime minister.
The fact is that they don't and we shouldn't assert that they do.
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.
There are few factors that could make him undesirable: few would dare to assert that they do not like Bowie or that they cannot find a point of connection with his work," concluded Waizel.
I've recently heard many commentators assert that they don't need their child benefit.
The plaintiffs assert that they did not know that their relatives were to be buried on top of construction debris.
They assert that they did not understand Madoff's investment strategy, but also that they did not question his distinctively reliable returns.
Many of the people assert that they did not know they were going to be asked to join the Herbalife network.
While the Mets assert that they did not know Beltran was having surgery the next day and that he did so without their consent, Beltran issued a statement Thursday night saying he spoke to Mets General Manager Omar Minaya on Tuesday about the planned surgery and that Minaya "just wished me well".
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.
