A museum in China has a problem. It seems to have a few fakes in its vast collection. Well, as many as 40,000. Everything it owns may be nothing more than a mass of crude forgeries.

Wei Yingjun, a consultant to the Jibaozhai Museum in Jizhou, about 150 miles south of Beijing, insists the situation is not that bad. He is "quite positive" that 80 or even more pieces out of tens of thousands in the museum are authentic.

In spite of this sterling defence, regional authorities in Hebei province have closed the museum amid a national scandal driven by some very free speech on China's internet. One online satirist suggested it should reopen as a museum of fakes – "If you can't be the best, why not be the worst?"

Maybe that's a good idea. All museums have a couple of fakes in their collections. Sometimes they own up to them, sometimes they put any dubious artefacts in a dark storeroom – and sometimes they don't know. But a collection that its accusers claim is entirely inauthentic is in its way a masterpiece of museology.

It's not like Jibaozhai is a small museum – it has 12 vast halls and cost 60 million yuan (about £6m) to build, opening its doors in 2010 during a culture boom that is seeing about 100 museums open every year across China. Unfortunately, it's hard to fill that many museums, and China also has a prolific faking industry. Art factories export low-cost fake Rembrandt and Van Goghs, while antique shops are full of eye-fooling replicas of classical Chinese art.

In one of his provocative works, Ai Weiwei smashes what appears to be a priceless historic vase. He is drawing attention to modern China's uneasy relationship to its long cultural past. This is a land with a continuous art tradition going back to prehistoric times – yet this creative past was severed from the present by the revolution of the 20th century. Surely the demand for museums across China reflects a desire to reconnect with a great heritage. The museum of fakes may be an absurd side-effect. But the angry and precise criticism that exposed it is a triumph of citizenship.