According to a motion filed by federal prosecutors on Thursday, the quandary arose last summer when such videos were posted of Henry T. Nicholas, III, the co-founder and former CEO of Broadcom (BRCM), the high-profile, fabless semiconductor company based in Irvine, California.

(Last Thursday Nicholas pleaded not guilty to two federal indictments, one charging options backdating and the other conspiracy to distribute drugs, including MDMA (ecstacy), methamphetamine, and cocaine.)

In August 2007 Nicholas attorney Susan Szabo of Munger Tolles & Olson wrote e-mails and faxes to YouTube and parent Google (GOOG) demanding they take down a video of Nicholas, which, she said, invaded his privacy.

A YouTube support rep e-mailed Szabo back explaining that the company couldn’t process a privacy complaint “based on what a video ‘purports’ to portray,” so he invited her to confirm that the video really did show her client in a private setting without his consent.

Szabo complied: “I can confirm that the video portrays my client and that the video was taken surreptitiously in his bedroom, without his knowledge and consent, and that any distribution of the video is without his consent.”

Now, in a motion asking that Nicholas be detained pending his trial on the two indictments, the government cites the video – which, it claims, shows Nicholas using drugs at a time when he knew the government was investigating him and when he was publicly denying drug use to the media – as tending to show that Nicholas presents a risk to the community and a flight risk. Prosecutors write: “There can be no doubt it was defendant in the video as his attorneys sent an e-mail and letter to YouTube confirming that the person in the video using drugs is, in fact, defendant.” (The judge ultimately ordered certain “home detention” measures for Nicholas.)

An e-mail to attorney Szabo was not immediately returned. Nicholas’s criminal defense attorney, Brendan Sullivan, wrote: “I adhere to a policy that I should not discuss matters in litigation.”

The government’s 18-page detention motion, with 100 pages of appended exhibits, also levels a variety of other unflattering accusations beyond those already contained in the indictments. During a June 2007 flight on one of his private jets, for instance, Nicholas allegedly accused a “longtime friend, personal attorney, and employee” of wearing a “wire”; threatened to “chase him to the ends of the earth” if the friend “screwed” him; and then struck the friend in the face, causing him to fall to the ground.

The papers also allege that in November 2007 Nicholas, while driving with his son, crashed his black Lamborghini into a lamp post while returning from a Shake Shack. He switched cars with a security staffer in his convoy and then left the scene while the staffer waited for the police and took the rap. Through an attorney, Nicholas later admitted to local police that he’d been driving the Lamborghini, but claimed that the security staffer had suggested Nicholas drive home for “security reasons,” and that Nicholas had never intended that the staffer take responsibility for the crash. (The staffer, according to prosecutors, has refused to testify about the incident notwithstanding an immunity order, and is currently incarcerated on contempt charges.)

Nicholas stepped down as Broadcom’s CEO and co-chairman in 2003, explaining in a statement that he wanted “to attend to serious family matters.”