As a half dozen wealthy Bay Area parents appeared in Boston federal court Friday, the Mill Valley founder and former managing partner of a global private equity firm claimed he never used a “side door” to get his son accepted to USC as a football recruit, answering allegations that he participated in a college admissions scam.

William McGlashan Jr., 55, argued in court records that his 18-year-old son, who has been diagnosed with learning disabilities, is still in high school and withdrew his college applications. But U.S. District Court Magistrate M. Page Kelley denied his request to go on a family vacation to Mexico next month, saying there was “some risk of flight,” according to Reuters.

McGlashan’s arguments represent one of the first defenses from the 13 wealthy Bay Area parents caught up in the nationwide scandal. But the claims conflict with transcripts provided by prosecutors of wiretapped conversations, in which the Mill Valley dad expressed interest in the “side door” bribery option. He has been freed on $1 million bail and forced to relinquish his passport.

McGlashan appeared Friday at the U.S. District Court in Boston for an initial appearance, along with five other Bay Area parents. All of them face a single charge of conspiracy to commit mail fraud and honest services mail fraud. They are among 33 high-profile parents, from Hollywood actresses to a vineyard owner and a fashion designer, charged in the case.

Earlier this month, federal prosecutors announced charges against ringleader William Rick Singer, accusing him of organizing an operation to funnel large sums of money from rich parents through his bogus charity, to bribe coaches at elite colleges and help the parents’ offspring cheat on entrance exams. Singer and two coaches have pleaded guilty in the scandal that has enraged parents and students who work honestly to get into increasingly competitive universities.

Prosecutors allege McGlashan, who was placed on indefinite administrative leave by his firm shortly after the scandal broke, paid $50,000 for Singer to get a proctor to correct his son’s ACT answers after the boy took the test. His son received a score of 34, out of 36, on the test in late 2017.

McGlashan inquired about getting a proctor to cheat on the tests for his two younger kids as well, prosecutors allege. The feds say his son sent the fraudulently obtained score with his application to Northeastern University in Boston, as well.

But while McGlashan’s attorneys argued that he never cut a check for a coaching bribe, prosecutors allege in court records that the Mill Valley father was more than willing to pay $250,000 to go that route, too. After Singer explained the process to him in conversations wiretapped last summer and included in the charging documents, McGlashan allegedly responded: “I would do that in a heartbeat.”

Singer explained how they would get around the fact that McGlashan’s son never played football, and that his high school didn’t even offer the sport, by faking his athletic credentials.

“I’m gonna make him a kicker/punter and they’re gonna walk him through with (a) football, and I’ll get a picture and figure out how to Photoshop and stuff,” Singer said in a voicemail to McGlashan, according to court records.

“Let me look through what I have. Pretty funny,” McGlashan allegedly said in a recorded call after Singer asked him for photographs of his son playing sports. “The way the world works these days is unbelievable.”

Singer told him the $250,000 bribe would give his son a 90 percent chance of admission to USC, according to prosecutors. The prosecutors do not allege that McGlashan ever went through with paying that money.

“Mr. McGlashan is alleged to have made a single payment of $50,000, and there is no allegation that Mr. McGlashan’s son ever attended a university based on any of the alleged conduct,” his attorney, Jack Pirozzolo, wrote in court documents. “And that is because Mr. McGlashan did not pay for the use of a so-called ‘side door’ to obtain admission for his son at USC or any other college.”

His attorneys argued that McGlashan should be allowed to travel for family and business reasons because of his close ties to the Marin County area, adding that “all three of the McGlashans’ children attend highly regarded local schools.”

“Mr. McGlashan is not going to abandon his immediate and extended family, and endanger hard-earned business relationships, by fleeing from a charge that he intends to vigorously contest,” Pirozzolo wrote. “He also understands that flight would be ‘ill-considered’ because this matter has been heavily publicized and sensationalized.”

Prosecutor Eric Rosen disagreed and recommended McGlashan spend his vacation domestically, such as at his $12 million home in Big Sky, Mont. The judge agreed, according to Reuters, saying, “I’m sorry to disappoint the family, but I’m not going to allow the vacation.”

The other Bay Area parents appearing Friday in Boston court were Todd and Diane Blake, of Ross, an entrepreneur and retail merchandising executive, respectively; Agustin Huneeus Jr., of San Francisco, a wine businessman; Marjorie Klapper, of Menlo Park, a jewelry business owner; and Marci Palatella, of Hillsborough, a beverage distribution owner.

The appearances Friday were largely a formality. The defendants did not enter a plea and the judge recited charges and maximum sentences, while advising the defendants of their rights.

The other defendants appearing Friday included Miami developer Robert Zangrillo, and Gregory Abbott, the founder and chairman of International Dispensing Corp. and his wife, Marcia Abbott.

On Thursday, former Yale University women’s soccer coach Rudy Meredith became the third person to plead guilty in the case. Former Stanford sailing coach John Vandemoer also pleaded guilty to accepting bribes earlier this month.

The Associated Press contributed to this report.

Matthias Gafni is a San Francisco Chronicle staff writer. Email: matthias.gafni@sfchronicle.com Twitter: @mgafni