Take Zerkala, one of several night clubs aimed at gays in the city. Offering a male striptease show among other entertainments, it is situated in the shadow of the mayor's office, making his apparent ignorance even less explicable.
"I've been here a few times," said Elena, 31, a lesbian, who has lived with her partner in Sochi for two years. "It's fun. This city is cool, definitely more relaxed than many places in Russia."
Then there is the Oblaka Hotel, which promises "fun, hedonism, old friends and new faces". It is nine miles from Putin's palatial Sochi residence, from where he has overseen the £31?billion Olympic constructions, the costliest ever.
"This gay hotel is run on a high European level. I've travelled all around Europe, and while I don't like the tone of the Russian debate on homosexuality and the persecution people can face, this place is somewhere you can relax," said Dima, 27, an entrepreneur from Moscow who stayed here last summer.
Another more famous gay club - Mayak - offers nightly drag shows for up to 400 customers in a dimly lit, one-storey building close to the seafront. There is no sign outside because it has been ripped down so often by homophobic youths.
The dancers include a Muslim former butcher, an Armenian who also owns a strip club, and a Ukrainian who loves to sing like Whitney Houston and dress like Adele. In a gold sequin dress, drag queen Andrei Kavaltshian, 44, is well known in Sochi. He powders his cleavage before risking a joke about Putin: "Our president has sensual lips and such a toned body."
The mayor's strange lack of knowledge is tackled by Andrei Tanichev, co-owner of the Mayak.
"There are many gays in Sochi, more than in most Russian cities," he said. "Our mayor knows this. He is fully aware of our club, and was in touch with us long before this TV programme."
Mr Tanichev, openly in a relationship with another man, said he had attended meetings with the mayor over improving the gloomy lighting outside his club.
"He invited us to his office. The major knows we are a gay club and there was no problem about it. We have discussed matters of safety and tolerance with him. About a month before this BBC story, there was a meeting in Sochi when the mayor invited representatives of all ethnic communities for a discussion on tolerance towards gay people who attend the Winter Olympics."
So how did the mayor come to make his claim?
Mr Tanichev's explanation is that the BBC mangled the meaning of the politician's words.
He has been told Mr Pakhomov was under the impression he had been asked whether there were gay activists or gay organisations in Sochi.
A source in the mayor's office said: "The phrase was taken out of context, because the next thing he said was that naturally there are gay people in Sochi. He was saying that we don't parade it - for example, we don't have gay parades."
- DAILY MAIL