Those who recognize it fail to defer to the main temple proper and therefore perpetuate an untruth.
There is 1 Shaolin Temple. That is the one at Songshan.
The remains of the temple found in Fujian were not set as Shaolin. It was a buddhist temple that got destroyed during the 300 years of Qing reign.
The qing destroyed literally hundreds and hundreds of temples that they felt might have too much wealth power or influence.
You see, Mahayana buddhism was strong in China. It promised that anyone could achieve Nirvana through continued acts of merit. So people gave great amounts of money and stuffs to buddhist temples to get that merit and subsequently, the buddhist monasteries and temples were soon rivaling the government of the day itself.
And so, temples were rubbed out, their wealth taken and the monks spread out or killed. Turbulent times.
When it comes to history, there are better sources than tall stories from the kwoon.