If imitation is the sincerest form of flattery, Apple should be crimson. As Mitt Romney observed in the second presidential debate, there are "even counterfeit Apple stores in China".

In the best-known case, in Kunming last year, the boss had gone to some lengths to kit out the store and staff in line with Apple design. Blue T-shirted employees believed they were working at a genuine branch.

The resulting headlines prompted a crackdown and the closure of at least a couple of stores for trading without a licence – but there are plenty more. Not all are masquerading as official Apple outlets, and those that do are not always convincing. It's hard to imagine the company endorsing the cheery slogan at this recently spotted retailer: "iPhone 5: because you have more money than sense".

And while Romney claimed the stores were selling counterfeit goods, most are actually selling genuine Apple products – often grey-market imports from Hong Kong – Charlie Custer, an editor at Tech In Asia, pointed out.

"Apple is getting the money one way or another," he said. People are often too impatient to wait until Apple has approval from Chinese authorities for products to be used on Chinese networks, as well as wanting the lower prices. And Apple has been relatively slow to roll out genuine stores on the mainland.

At the same time, the enforcement of rights tends to be spasmodic. "The intellectual property [situation] is improving, but not as fast as many people would like," said Duncan Clark of the BDA China business consultancy, and formerly chairman of the British Chamber of Commerce in China. "There are periodic crackdowns, but there's still a long way to go."

Clark suggested that changing demand might be having more of an impact than curbs on the supply of fakes. "When it comes to very desirable products, Chinese consumers absolutely know the difference and will pay above the odds to get the real thing," he said.

The surge in fake Apple stores in large part reflects demand for the genuine products. Custer described the iPhone as "a perfect status symbol that's still in the price range of a lot of people"; unlike, say, a Mercedes. White-collar buyers want the real deal.

But for the others, there are plenty of products – and not just phones and gadgets – that appear to be inspired by Apple. At the Guangzhou Sex Culture Festival this month, there were "iPed" sex toys and, this spring, "iPhone 5" ice creams – complete with a trademark symbol – appeared in convenience stores.

Even so, the blogger who first found the Kunming store pointed out that Applemania was not a uniquely Chinese phenomenon. Internet users mailed her images of fake stores from around the world, including one in New York.

"It is more of a global issue, but it doesn't create as nice a story as China ripping off Apple stores," she told the Wall Street Journal.

"[Mitt Romney] uses it as a shorthand to generate outrage about trade practices in China and as a shorthand that he will be quote-unquote 'tough on China'. It's a somewhat meaningless shorthand. I'm not entirely sure he knows what he's referring to at this point."