Other figures seem off, but are harder to verify. Ozy told Axios in January that the company’s newsletters had “more than 20 million subscribers.” By comparison, the Morning Brew, a successful newsletter-based business media company, says it has three million subscribers.

“I’ve never heard an explanation of Ozy that made sense to me,” said Brian Morrissey, the former editor in chief of Digiday, a publication covering digital media and the tech industry, who now writes The Rebooting, a newsletter focused on media businesses. He said he was struck by the company’s claims, adding, “then you do the gut check, and never once in my life has a piece of content from Ozy crossed into my world organically.”

Mr. Watson said in the email that he understood the skepticism but that Ozy’s growth “has been completely real.”

“It’s the result of our team acting pretty fearlessly to launch and grow five newsletters, 12 TV shows, six podcasts, now four annual festivals starting next year, and the Ozy Genius Awards,” he said. “Each of our verticals is thriving, and we stand completely behind our numbers and performance.”

But the company has overstated its success on big platforms, as well as the strength of its relationship with them. Billboards in Los Angeles, for instance, say that “The Carlos Watson Show” is “Amazon Prime’s First Talk Show.” In fact, Ozy has been uploading the show to the platform through a service called “video direct,” which many YouTube channels use to pick up extra views on Amazon’s video platform but which receives no promotion from Amazon Prime Video itself. Last week, Amazon complained that Ozy’s use of its brand name on the billboards violated promotion guidelines; Ozy apologized and promised to take down the signs, an Amazon Prime Video spokesman said.

Mr. Watson said the billboards’ claim was “accurate,” but confirmed that the company would stop making that claim at Amazon’s request.

Ozy also markets Mr. Watson’s show as “the fastest-growing talk show in YouTube history,” a quote that appears to be drawn from a question posed by a host of ABC’s “Good Morning America” during Mr. Watson’s appearance last year. Asked about the claim, Mr. Watson said that his show had more views than any other “premium daily talk show we’ve been able to identify that was launched on YouTube.”