There were many problems with all this. For one, much of this was not new: The New York Times had reported in October what Mr. Sussmann had told the C.I.A. about data suggesting that Russian-made smartphones, called YotaPhones, had been connecting to networks at Trump Tower and the White House, among other places.

The conservative media also skewed what the filing said. For example, Mr. Durham’s filing never used the word “infiltrate.” And it never claimed that Mr. Joffe’s company was being paid by the Clinton campaign.

Most important, contrary to the reporting, the filing never said the White House data that came under scrutiny was from the Trump era. According to lawyers for David Dagon, a Georgia Institute of Technology data scientist who helped develop the Yota analysis, the data — so-called DNS logs, which are records of when computers or smartphones have prepared to communicate with servers over the internet — came from Barack Obama’s presidency.

“What Trump and some news outlets are saying is wrong,” said Jody Westby and Mark Rasch, both lawyers for Mr. Dagon. “The cybersecurity researchers were investigating malware in the White House, not spying on the Trump campaign, and to our knowledge all of the data they used was nonprivate DNS data from before Trump took office.”